Introduction to Riemannian manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
[2018]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Graduate texts in mathematics
176 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xiii, 437 Seiten Illustrationen |
| ISBN: | 9783319917542 9783030801069 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV045403804 | ||
| 003 | DE-604 | ||
| 005 | 20240223 | ||
| 007 | t | ||
| 008 | 190117s2018 a||| |||| 00||| eng d | ||
| 020 | |a 9783319917542 |c hbk |9 978-3-319-91754-2 | ||
| 020 | |a 9783030801069 |c pbk |9 978-3-030-80106-9 | ||
| 035 | |a (OCoLC)1085413534 | ||
| 035 | |a (DE-599)BVBBV045403804 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-355 |a DE-11 |a DE-20 |a DE-19 |a DE-739 |a DE-384 | ||
| 082 | 0 | |a 516.373 |b L224 |2 21 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a MAT 537f |2 stub | ||
| 084 | |a 53C20 |2 msc | ||
| 100 | 1 | |a Lee, John M. |d 1950- |e Verfasser |0 (DE-588)122260880 |4 aut | |
| 240 | 1 | 0 | |a Riemannian manifolds (an introduction to curvature) |
| 245 | 1 | 0 | |a Introduction to Riemannian manifolds |c John M. Lee |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York |b Springer |c [2018] | |
| 300 | |a xiii, 437 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 176 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Geometría de Riemann | |
| 650 | 0 | 7 | |a Krümmung |0 (DE-588)4128765-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannscher Raum |0 (DE-588)4128295-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Riemannscher Raum |0 (DE-588)4128295-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |D s |
| 689 | 1 | 1 | |a Krümmung |0 (DE-588)4128765-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-91755-9 |
| 830 | 0 | |a Graduate texts in mathematics |v 176 |w (DE-604)BV000000067 |9 176 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030789837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030789837 | ||
Datensatz im Suchindex
| _version_ | 1804179274461085696 |
|---|---|
| adam_text | Contents Preface............................................................................................................. v 1 What Is Curvature?................................................................................... The Euclidean Plane..................................................................................... Surfaces in Space......................................................................................... Curvature in Higher Dimensions................................................................ 1 1 4 7 2 Riemannian Metrics................................................................................... Definitions..................................................................................................... Methods for Constructing Riemannian Metrics........................................ Basic Constructions on Riemannian Manifolds........................................ Lengths and Distances ................................................................................ Pseudo-Riemannian Metrics......................................................................... Other Generalizations of Riemannian Metrics........................................... Problems........................................................................................................ 9 9 15 25 33 40 46 47 3 Model Riemannian Manifolds.................................................................. Symmetries of Riemannian Manifolds...................................................... Euclidean
Spaces......................................................................................... Spheres.......................................................................................................... Hyperbolic Spaces....................................................................................... Invariant Metrics on Lie Groups................................................................ Other Homogeneous Riemannian Manifolds............................................. Model Pseudo-Riemannian Manifolds...................................................... Problems........................................................................................................ 55 55 57 58 62 67 72 79 80 4 Connections................................................................................................... The Problem of Differentiating Vector Fields.......................................... Connections................................................................................................... Covariant Derivatives of Tensor Fields .................................................... Vector and Tensor Fields Along Curves.................................................... 85 85 88 95 100 xi
xii Contents Geodesics........................................................................................................ Parallel Transport.......................................................................................... Pullback Connections................................................................................... Problems........................................................................................................ 103 105 110 Ill 5 The Levi-Civita Connection.................................................................... The Tangential Connection Revisited......................................................... Connections on Abstract Riemannian Manifolds...................................... The Exponential Map................................................................................... Normal Neighborhoods and Normal Coordinates................................... Tubular Neighborhoods and Fermi Coordinates...................................... Geodesics of the Model Spaces.................................................................. Euclidean and Non-Euclidean Geometries......................... Problems................................................................................ 1..................... 115 115 117 126 131 133 136 142 145 6 Geodesics and Distance.............................................................................. Geodesics and Minimizing Curves............................................................. Uniformly Normal
Neighborhoods............................................................. Completeness................................................................................................. Distance Functions....................................................................................... Semigeodesic Coordinates........................................................................... Problems........................................................................................................ 151 151 163 166 174 181 185 7 Curvature..................................................................................................... Local Invariants............................................................................................ The Curvature Tensor.................................................................................. Flat Manifolds.............................................................................................. Symmetries of the Curvature Tensor........................................................ The Ricci Identities....................................................................................... Ricci and Scalar Curvatures......................................................................... The Weyl Tensor.......................................................................................... Curvatures of Conformally Related Metrics............................................. Problems........................................................................................................ 193 193 196 199 202 205 207
212 216 222 8 Riemannian Submanifolds......................................................................... The Second Fundamental Form.................................................................. Hypersurfaces................................................................................................. Hypersurfaces in Euclidean Space............................................................. Sectional Curvatures..................................................................................... Problems........................................................................................................ 225 225 234 244 250 255 9 The Gauss-Bonnet Theorem.................................................................... 263 Some Plane Geometry................................................................................... 263 The Gauss-Bonnet Formula....................................................................... 271
Contents xiii The Gauss-Bonnet Theorem....................................................................... 276 Problems........................................................................................................ 281 10 Jacobi Fields................................................................................................ The Jacobi Equation..................................................................................... Basic Computations with Jacobi Fields.................................................... Conjugate Points............................................................................................ The Second Variation Formula.................................................................. Cut Points............................................................................. Problems........................................................................................................ 283 284 287 297 300 307 313 11 Comparison Theory..................................... Jacobi Fields, Hessians, and Riccati Equations........................................ Comparisons Based on Sectional Curvature............................................. Comparisons Based on Ricci Curvature.................................................... Problems........................................................................................................ 319 320 327 336 342 12 Curvature and Topology........................................................................... Manifolds of Constant
Curvature................................................................ Manifolds of Nonpositive Curvature......................................................... Manifolds of Positive Curvature................................................................ Problems........................................................................................................ 345 345 352 361 368 Appendix A: Review of Smooth Manifolds.................................................... Topological Preliminaries............................................................................ Smooth Manifolds and Smooth Maps........................................................ Tangent Vectors........................................................................................... Submanifolds.................................................................................................. Vector Bundles.............................................................................................. The Tangent Bundle and Vector Fields...................................................... Smooth Covering Maps................................................................................ 371 371 374 376 378 382 384 388 Appendix B: Review of Tensors....................................................................... Tensors on a Vector Space.......................................................................... Tensor Bundles and Tensor Fields............................................................ Differential Forms and
Integration.............................................................. Densities......................................................................................................... 391 391 396 400 405 Appendix C: Review of Lie Groups................................................................. Definitions and Properties............................................................................ The Lie Algebra of a Lie Group................................................................. Group Actions on Manifolds....................................................................... 407 407 408 411 References............................................................................................................. 415 Notation Index....................................................................................................... 419 Subject Index......................................................................................................... 423
|
| any_adam_object | 1 |
| author | Lee, John M. 1950- |
| author_GND | (DE-588)122260880 |
| author_facet | Lee, John M. 1950- |
| author_role | aut |
| author_sort | Lee, John M. 1950- |
| author_variant | j m l jm jml |
| building | Verbundindex |
| bvnumber | BV045403804 |
| classification_rvk | SK 370 |
| classification_tum | MAT 537f |
| ctrlnum | (OCoLC)1085413534 (DE-599)BVBBV045403804 |
| dewey-full | 516.373 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.373 |
| dewey-search | 516.373 |
| dewey-sort | 3516.373 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02073nam a2200505 cb4500</leader><controlfield tag="001">BV045403804</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240223 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">190117s2018 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783319917542</subfield><subfield code="c">hbk</subfield><subfield code="9">978-3-319-91754-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783030801069</subfield><subfield code="c">pbk</subfield><subfield code="9">978-3-030-80106-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1085413534</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV045403804</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-83</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.373</subfield><subfield code="b">L224</subfield><subfield code="2">21</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="084" ind1=" " ind2=" "><subfield code="a">MAT 537f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">53C20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lee, John M.</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122260880</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Riemannian manifolds (an introduction to curvature)</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to Riemannian manifolds</subfield><subfield code="c">John M. Lee</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Springer</subfield><subfield code="c">[2018]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiii, 437 Seiten</subfield><subfield code="b">Illustrationen</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">176</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometría de Riemann</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Krümmung</subfield><subfield code="0">(DE-588)4128765-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannsche Geometrie</subfield><subfield code="0">(DE-588)4128462-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannscher Raum</subfield><subfield code="0">(DE-588)4128295-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Riemannscher Raum</subfield><subfield code="0">(DE-588)4128295-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Riemannsche Geometrie</subfield><subfield code="0">(DE-588)4128462-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Krümmung</subfield><subfield code="0">(DE-588)4128765-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-319-91755-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">176</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">176</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030789837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030789837</subfield></datafield></record></collection> |
| id | DE-604.BV045403804 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:17:16Z |
| institution | BVB |
| isbn | 9783319917542 9783030801069 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030789837 |
| oclc_num | 1085413534 |
| open_access_boolean | |
| owner | DE-83 DE-355 DE-BY-UBR DE-11 DE-20 DE-19 DE-BY-UBM DE-739 DE-384 |
| owner_facet | DE-83 DE-355 DE-BY-UBR DE-11 DE-20 DE-19 DE-BY-UBM DE-739 DE-384 |
| physical | xiii, 437 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Lee, John M. 1950- Verfasser (DE-588)122260880 aut Riemannian manifolds (an introduction to curvature) Introduction to Riemannian manifolds John M. Lee Second edition New York Springer [2018] xiii, 437 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 176 Hier auch später erschienene, unveränderte Nachdrucke Geometría de Riemann Krümmung (DE-588)4128765-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 s DE-604 Riemannsche Geometrie (DE-588)4128462-8 s Krümmung (DE-588)4128765-4 s Erscheint auch als Online-Ausgabe 978-3-319-91755-9 Graduate texts in mathematics 176 (DE-604)BV000000067 176 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030789837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lee, John M. 1950- Introduction to Riemannian manifolds Graduate texts in mathematics Geometría de Riemann Krümmung (DE-588)4128765-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4128765-4 (DE-588)4128462-8 (DE-588)4128295-4 |
| title | Introduction to Riemannian manifolds |
| title_alt | Riemannian manifolds (an introduction to curvature) |
| title_auth | Introduction to Riemannian manifolds |
| title_exact_search | Introduction to Riemannian manifolds |
| title_full | Introduction to Riemannian manifolds John M. Lee |
| title_fullStr | Introduction to Riemannian manifolds John M. Lee |
| title_full_unstemmed | Introduction to Riemannian manifolds John M. Lee |
| title_short | Introduction to Riemannian manifolds |
| title_sort | introduction to riemannian manifolds |
| topic | Geometría de Riemann Krümmung (DE-588)4128765-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Geometría de Riemann Krümmung Riemannsche Geometrie Riemannscher Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030789837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT leejohnm riemannianmanifoldsanintroductiontocurvature AT leejohnm introductiontoriemannianmanifolds |