Riemannian geometry in an orthogonal frame :: from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 /
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English Russian |
| Veröffentlicht: |
River Edge, NJ :
World Scientific,
©2001.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition |
| Beschreibung: | Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalʹnom repere. |
| Beschreibung: | 1 online resource (xvii, 259 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812799715 9812799710 1281948039 9781281948038 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn261122572 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 081007s2001 njua ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d YDXCP |d OCLCQ |d IDEBK |d OCLCA |d OCLCQ |d OCLCF |d NLGGC |d OCLCQ |d INTCL |d COCUF |d OCLCQ |d U3W |d OCLCQ |d VTS |d AGLDB |d INT |d OCLCQ |d STF |d M8D |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 815754178 | ||
| 020 | |a 9789812799715 |q (electronic bk.) | ||
| 020 | |a 9812799710 |q (electronic bk.) | ||
| 020 | |a 1281948039 | ||
| 020 | |a 9781281948038 | ||
| 035 | |a (OCoLC)261122572 |z (OCoLC)815754178 | ||
| 041 | 1 | |a eng |h rus | |
| 050 | 4 | |a QA649 |b .C3413 2001eb | |
| 072 | 7 | |a MAT |x 012020 |2 bisacsh | |
| 072 | 7 | |a PBMP |2 bicssc | |
| 082 | 7 | |a 516.3/73 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Cartan, Elie, |d 1869-1951. |1 https://id.oclc.org/worldcat/entity/E39PBJh8JTkFmVYtvcdQWc3PcP |0 http://id.loc.gov/authorities/names/n83005890 | |
| 240 | 1 | 0 | |a Rimanova geometrii︠a︡ v ortogonalʹnom repere. |l English |
| 245 | 1 | 0 | |a Riemannian geometry in an orthogonal frame : |b from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / |c translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern. |
| 260 | |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xvii, 259 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalʹnom repere. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition | ||
| 505 | 0 | 0 | |g Machine generated contents note: |t Method of Moving Frames -- |t Theory of Pfaffian Forms -- |t Integration of Systems of Pfaffian Differential Equations -- |t Generalization -- |t Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] -- |t Fundamental Theorem of Metric Geometry -- |t Vector Analysis in an n-Dimensional Euclidean Space -- |t Fundamental Principles of Tensor Algebra -- |t Tensor Analysis -- |t Notion of a Manifold -- |t Locally Euclidean Riemannian Manifolds -- |t Euclidean Space Tangent at a Point -- |t Osculating Euclidean Space -- |t Euclidean Space of Conjugacy Along a Line -- |t Space with a Euclidean Connection -- |t Riemannian Curvature of a Manifold -- |t Spaces of Constant Curvature -- |t Geometric Construction of a Space of Constant Curvature -- |t Variational Problems for Geodesics -- |t Distribution of Geodesics Near a Given Geodesic -- |t Geodesic Surfaces -- |t Lines in a Riemannian Manifold -- |t Surfaces in a Three-Dimensional Riemannian Manifold -- |t Forms of Laguerre and Darboux. |
| 650 | 0 | |a Geometry, Riemannian. |0 http://id.loc.gov/authorities/subjects/sh85054159 | |
| 650 | 6 | |a Géométrie de Riemann. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
| 650 | 7 | |a Geometry, Riemannian |2 fast | |
| 650 | 7 | |a Geometria riemanniana. |2 larpcal | |
| 700 | 1 | |a Finikov, S. P. |q (Sergeĭ Pavlovich), |d 1883-1964. |1 https://id.oclc.org/worldcat/entity/E39PBJpYq87kgYgQxJwHwFrwmd |0 http://id.loc.gov/authorities/names/n84804177 | |
| 758 | |i has work: |a Riemannian geometry in an orthogonal frame (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFGwJFGG4BR33hyPcvMxCP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Cartan, Elie, 1869-1951. |s Rimanova geometrii︠a︡ v ortogonalʹnom repere. English. |t Riemannian geometry in an orthogonal frame. |d River Edge, NJ : World Scientific, ©2001 |z 981024746X |z 9789810247461 |w (DLC) 2002277436 |w (OCoLC)49356062 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235770 |3 Volltext |
| 938 | |a EBSCOhost |b EBSC |n 235770 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 194803 | ||
| 938 | |a YBP Library Services |b YANK |n 2889330 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn261122572 |
|---|---|
| _version_ | 1816881678579138560 |
| adam_text | |
| any_adam_object | |
| author | Cartan, Elie, 1869-1951 |
| author2 | Finikov, S. P. (Sergeĭ Pavlovich), 1883-1964 |
| author2_role | |
| author2_variant | s p f sp spf |
| author_GND | http://id.loc.gov/authorities/names/n83005890 http://id.loc.gov/authorities/names/n84804177 |
| author_facet | Cartan, Elie, 1869-1951 Finikov, S. P. (Sergeĭ Pavlovich), 1883-1964 |
| author_role | |
| author_sort | Cartan, Elie, 1869-1951 |
| author_variant | e c ec |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA649 |
| callnumber-raw | QA649 .C3413 2001eb |
| callnumber-search | QA649 .C3413 2001eb |
| callnumber-sort | QA 3649 C3413 42001EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Method of Moving Frames -- Theory of Pfaffian Forms -- Integration of Systems of Pfaffian Differential Equations -- Generalization -- Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] -- Fundamental Theorem of Metric Geometry -- Vector Analysis in an n-Dimensional Euclidean Space -- Fundamental Principles of Tensor Algebra -- Tensor Analysis -- Notion of a Manifold -- Locally Euclidean Riemannian Manifolds -- Euclidean Space Tangent at a Point -- Osculating Euclidean Space -- Euclidean Space of Conjugacy Along a Line -- Space with a Euclidean Connection -- Riemannian Curvature of a Manifold -- Spaces of Constant Curvature -- Geometric Construction of a Space of Constant Curvature -- Variational Problems for Geodesics -- Distribution of Geodesics Near a Given Geodesic -- Geodesic Surfaces -- Lines in a Riemannian Manifold -- Surfaces in a Three-Dimensional Riemannian Manifold -- Forms of Laguerre and Darboux. |
| ctrlnum | (OCoLC)261122572 |
| dewey-full | 516.3/73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
| dewey-search | 516.3/73 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05351cam a2200565 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn261122572</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">081007s2001 njua ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCA</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">NLGGC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">INTCL</subfield><subfield code="d">COCUF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">AGLDB</subfield><subfield code="d">INT</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">STF</subfield><subfield code="d">M8D</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">815754178</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812799715</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812799710</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1281948039</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781281948038</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)261122572</subfield><subfield code="z">(OCoLC)815754178</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA649</subfield><subfield code="b">.C3413 2001eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">012020</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">PBMP</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">516.3/73</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cartan, Elie,</subfield><subfield code="d">1869-1951.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJh8JTkFmVYtvcdQWc3PcP</subfield><subfield code="0">http://id.loc.gov/authorities/names/n83005890</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Rimanova geometrii︠a︡ v ortogonalʹnom repere.</subfield><subfield code="l">English</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Riemannian geometry in an orthogonal frame :</subfield><subfield code="b">from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 /</subfield><subfield code="c">translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2001.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xvii, 259 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalʹnom repere.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">Machine generated contents note:</subfield><subfield code="t">Method of Moving Frames --</subfield><subfield code="t">Theory of Pfaffian Forms --</subfield><subfield code="t">Integration of Systems of Pfaffian Differential Equations --</subfield><subfield code="t">Generalization --</subfield><subfield code="t">Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] --</subfield><subfield code="t">Fundamental Theorem of Metric Geometry --</subfield><subfield code="t">Vector Analysis in an n-Dimensional Euclidean Space --</subfield><subfield code="t">Fundamental Principles of Tensor Algebra --</subfield><subfield code="t">Tensor Analysis --</subfield><subfield code="t">Notion of a Manifold --</subfield><subfield code="t">Locally Euclidean Riemannian Manifolds --</subfield><subfield code="t">Euclidean Space Tangent at a Point --</subfield><subfield code="t">Osculating Euclidean Space --</subfield><subfield code="t">Euclidean Space of Conjugacy Along a Line --</subfield><subfield code="t">Space with a Euclidean Connection --</subfield><subfield code="t">Riemannian Curvature of a Manifold --</subfield><subfield code="t">Spaces of Constant Curvature --</subfield><subfield code="t">Geometric Construction of a Space of Constant Curvature --</subfield><subfield code="t">Variational Problems for Geodesics --</subfield><subfield code="t">Distribution of Geodesics Near a Given Geodesic --</subfield><subfield code="t">Geodesic Surfaces --</subfield><subfield code="t">Lines in a Riemannian Manifold --</subfield><subfield code="t">Surfaces in a Three-Dimensional Riemannian Manifold --</subfield><subfield code="t">Forms of Laguerre and Darboux.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometry, Riemannian.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054159</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Géométrie de Riemann.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Geometry</subfield><subfield code="x">Analytic.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometry, Riemannian</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometria riemanniana.</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Finikov, S. P.</subfield><subfield code="q">(Sergeĭ Pavlovich),</subfield><subfield code="d">1883-1964.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJpYq87kgYgQxJwHwFrwmd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n84804177</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Riemannian geometry in an orthogonal frame (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFGwJFGG4BR33hyPcvMxCP</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Cartan, Elie, 1869-1951.</subfield><subfield code="s">Rimanova geometrii︠a︡ v ortogonalʹnom repere. English.</subfield><subfield code="t">Riemannian geometry in an orthogonal frame.</subfield><subfield code="d">River Edge, NJ : World Scientific, ©2001</subfield><subfield code="z">981024746X</subfield><subfield code="z">9789810247461</subfield><subfield code="w">(DLC) 2002277436</subfield><subfield code="w">(OCoLC)49356062</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235770</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235770</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">194803</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2889330</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn261122572 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:32Z |
| institution | BVB |
| isbn | 9789812799715 9812799710 1281948039 9781281948038 |
| language | English Russian |
| oclc_num | 261122572 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xvii, 259 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Cartan, Elie, 1869-1951. https://id.oclc.org/worldcat/entity/E39PBJh8JTkFmVYtvcdQWc3PcP http://id.loc.gov/authorities/names/n83005890 Rimanova geometrii︠a︡ v ortogonalʹnom repere. English Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern. River Edge, NJ : World Scientific, ©2001. 1 online resource (xvii, 259 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalʹnom repere. Includes bibliographical references and index. Print version record. Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition Machine generated contents note: Method of Moving Frames -- Theory of Pfaffian Forms -- Integration of Systems of Pfaffian Differential Equations -- Generalization -- Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] -- Fundamental Theorem of Metric Geometry -- Vector Analysis in an n-Dimensional Euclidean Space -- Fundamental Principles of Tensor Algebra -- Tensor Analysis -- Notion of a Manifold -- Locally Euclidean Riemannian Manifolds -- Euclidean Space Tangent at a Point -- Osculating Euclidean Space -- Euclidean Space of Conjugacy Along a Line -- Space with a Euclidean Connection -- Riemannian Curvature of a Manifold -- Spaces of Constant Curvature -- Geometric Construction of a Space of Constant Curvature -- Variational Problems for Geodesics -- Distribution of Geodesics Near a Given Geodesic -- Geodesic Surfaces -- Lines in a Riemannian Manifold -- Surfaces in a Three-Dimensional Riemannian Manifold -- Forms of Laguerre and Darboux. Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Géométrie de Riemann. MATHEMATICS Geometry Analytic. bisacsh Geometry, Riemannian fast Geometria riemanniana. larpcal Finikov, S. P. (Sergeĭ Pavlovich), 1883-1964. https://id.oclc.org/worldcat/entity/E39PBJpYq87kgYgQxJwHwFrwmd http://id.loc.gov/authorities/names/n84804177 has work: Riemannian geometry in an orthogonal frame (Text) https://id.oclc.org/worldcat/entity/E39PCFGwJFGG4BR33hyPcvMxCP https://id.oclc.org/worldcat/ontology/hasWork Print version: Cartan, Elie, 1869-1951. Rimanova geometrii︠a︡ v ortogonalʹnom repere. English. Riemannian geometry in an orthogonal frame. River Edge, NJ : World Scientific, ©2001 981024746X 9789810247461 (DLC) 2002277436 (OCoLC)49356062 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235770 Volltext |
| spellingShingle | Cartan, Elie, 1869-1951 Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / Method of Moving Frames -- Theory of Pfaffian Forms -- Integration of Systems of Pfaffian Differential Equations -- Generalization -- Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] -- Fundamental Theorem of Metric Geometry -- Vector Analysis in an n-Dimensional Euclidean Space -- Fundamental Principles of Tensor Algebra -- Tensor Analysis -- Notion of a Manifold -- Locally Euclidean Riemannian Manifolds -- Euclidean Space Tangent at a Point -- Osculating Euclidean Space -- Euclidean Space of Conjugacy Along a Line -- Space with a Euclidean Connection -- Riemannian Curvature of a Manifold -- Spaces of Constant Curvature -- Geometric Construction of a Space of Constant Curvature -- Variational Problems for Geodesics -- Distribution of Geodesics Near a Given Geodesic -- Geodesic Surfaces -- Lines in a Riemannian Manifold -- Surfaces in a Three-Dimensional Riemannian Manifold -- Forms of Laguerre and Darboux. Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Géométrie de Riemann. MATHEMATICS Geometry Analytic. bisacsh Geometry, Riemannian fast Geometria riemanniana. larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054159 |
| title | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / |
| title_alt | Rimanova geometrii︠a︡ v ortogonalʹnom repere. Method of Moving Frames -- Theory of Pfaffian Forms -- Integration of Systems of Pfaffian Differential Equations -- Generalization -- Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j] -- Fundamental Theorem of Metric Geometry -- Vector Analysis in an n-Dimensional Euclidean Space -- Fundamental Principles of Tensor Algebra -- Tensor Analysis -- Notion of a Manifold -- Locally Euclidean Riemannian Manifolds -- Euclidean Space Tangent at a Point -- Osculating Euclidean Space -- Euclidean Space of Conjugacy Along a Line -- Space with a Euclidean Connection -- Riemannian Curvature of a Manifold -- Spaces of Constant Curvature -- Geometric Construction of a Space of Constant Curvature -- Variational Problems for Geodesics -- Distribution of Geodesics Near a Given Geodesic -- Geodesic Surfaces -- Lines in a Riemannian Manifold -- Surfaces in a Three-Dimensional Riemannian Manifold -- Forms of Laguerre and Darboux. |
| title_auth | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / |
| title_exact_search | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / |
| title_full | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern. |
| title_fullStr | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern. |
| title_full_unstemmed | Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / translated from Russian by Vladislav V. Goldberg ; foreword by S.S. Chern. |
| title_short | Riemannian geometry in an orthogonal frame : |
| title_sort | riemannian geometry in an orthogonal frame from lectures delivered by elie cartan at the sorbonne in 1926 27 |
| title_sub | from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 / |
| topic | Geometry, Riemannian. http://id.loc.gov/authorities/subjects/sh85054159 Géométrie de Riemann. MATHEMATICS Geometry Analytic. bisacsh Geometry, Riemannian fast Geometria riemanniana. larpcal |
| topic_facet | Geometry, Riemannian. Géométrie de Riemann. MATHEMATICS Geometry Analytic. Geometry, Riemannian Geometria riemanniana. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235770 |
| work_keys_str_mv | AT cartanelie rimanovageometriiavortogonalʹnomrepere AT finikovsp rimanovageometriiavortogonalʹnomrepere AT cartanelie riemanniangeometryinanorthogonalframefromlecturesdeliveredbyeliecartanatthesorbonnein192627 AT finikovsp riemanniangeometryinanorthogonalframefromlecturesdeliveredbyeliecartanatthesorbonnein192627 |