Sub-Riemannian geometry: general theory and examples
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel i...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2009
|
| Series: | Encyclopedia of mathematics and its applications
volume 126 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiii, 370 pages) |
| ISBN: | 9781139195966 |
| DOI: | 10.1017/CBO9781139195966 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941709 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2009 |||| o||u| ||||||eng d | ||
| 020 | |a 9781139195966 |c Online |9 978-1-139-19596-6 | ||
| 024 | 7 | |a 10.1017/CBO9781139195966 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781139195966 | ||
| 035 | |a (OCoLC)852654157 | ||
| 035 | |a (DE-599)BVBBV043941709 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 516.3/73 |2 22 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 100 | 1 | |a Calin, Ovidiu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sub-Riemannian geometry |b general theory and examples |c Ovidiu Calin, Der-chen Chang |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2009 | |
| 300 | |a 1 online resource (xiii, 370 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 126 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles | |
| 520 | |a Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry | ||
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 4 | |a Riemannian manifolds | |
| 650 | 4 | |a Geodesics (Mathematics) | |
| 650 | 4 | |a Submanifolds | |
| 700 | 1 | |a Chang, Der-chen E. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-89730-3 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781139195966 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350679 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9781139195966 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9781139195966 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804176883797983232 |
|---|---|
| any_adam_object | |
| author | Calin, Ovidiu |
| author_facet | Calin, Ovidiu |
| author_role | aut |
| author_sort | Calin, Ovidiu |
| author_variant | o c oc |
| building | Verbundindex |
| bvnumber | BV043941709 |
| classification_rvk | SK 370 |
| collection | ZDB-20-CBO |
| contents | Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles |
| ctrlnum | (ZDB-20-CBO)CR9781139195966 (OCoLC)852654157 (DE-599)BVBBV043941709 |
| 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 |
| doi_str_mv | 10.1017/CBO9781139195966 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02988nmm a2200469zcb4500</leader><controlfield tag="001">BV043941709</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2009 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139195966</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-139-19596-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781139195966</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781139195966</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)852654157</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941709</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/73</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Calin, Ovidiu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sub-Riemannian geometry</subfield><subfield code="b">general theory and examples</subfield><subfield code="c">Ovidiu Calin, Der-chen Chang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiii, 370 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Encyclopedia of mathematics and its applications</subfield><subfield code="v">volume 126</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Riemannian</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Riemannian manifolds</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geodesics (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Submanifolds</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chang, Der-chen E.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-89730-3</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781139195966</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350679</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139195966</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139195966</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941709 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139195966 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350679 |
| oclc_num | 852654157 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiii, 370 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Calin, Ovidiu Verfasser aut Sub-Riemannian geometry general theory and examples Ovidiu Calin, Der-chen Chang Cambridge Cambridge University Press 2009 1 online resource (xiii, 370 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 126 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry Geometry, Riemannian Riemannian manifolds Geodesics (Mathematics) Submanifolds Chang, Der-chen E. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-89730-3 https://doi.org/10.1017/CBO9781139195966 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Calin, Ovidiu Sub-Riemannian geometry general theory and examples Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles Geometry, Riemannian Riemannian manifolds Geodesics (Mathematics) Submanifolds |
| title | Sub-Riemannian geometry general theory and examples |
| title_auth | Sub-Riemannian geometry general theory and examples |
| title_exact_search | Sub-Riemannian geometry general theory and examples |
| title_full | Sub-Riemannian geometry general theory and examples Ovidiu Calin, Der-chen Chang |
| title_fullStr | Sub-Riemannian geometry general theory and examples Ovidiu Calin, Der-chen Chang |
| title_full_unstemmed | Sub-Riemannian geometry general theory and examples Ovidiu Calin, Der-chen Chang |
| title_short | Sub-Riemannian geometry |
| title_sort | sub riemannian geometry general theory and examples |
| title_sub | general theory and examples |
| topic | Geometry, Riemannian Riemannian manifolds Geodesics (Mathematics) Submanifolds |
| topic_facet | Geometry, Riemannian Riemannian manifolds Geodesics (Mathematics) Submanifolds |
| url | https://doi.org/10.1017/CBO9781139195966 |
| work_keys_str_mv | AT calinovidiu subriemanniangeometrygeneraltheoryandexamples AT changderchene subriemanniangeometrygeneraltheoryandexamples |