Riemannian geometry and geometric analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | 3. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 532 S. |
| ISBN: | 3540426272 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Foundational Material 1
1.1 Manifolds and Differentiable Manifolds 1
1.2 Tangent Spaces 5
1.3 Submanifolds 9
1.4 Riemannian Metrics 12
1.5 Vector Bundles 32
1.6 Integral Curves of Vector Fields. Lie Algebras 41
1.7 Lie Groups 50
1.8 Spin Structures 56
Exercises for Chapter 1 76
2. De Rham Cohomology and Harmonic Differential
Forms 79
2.1 The Laplace Operator 79
2.2 Representing Cohomology Classes by Harmonic Forms .... 87
2.3 Generalizations 96
Exercises for Chapter 2 97
3. Parallel Transport, Connections, and Covariant
Derivatives 101
3.1 Connections in Vector Bundles 101
3.2 Metric Connections. The Yang Mills Functional 110
3.3 The Levi Civita Connection 127
3.4 Connections for Spin Structures and the Dirac Operator ... 142
3.5 The Bochner Method 148
3.6 The Geometry of Submanifolds. Minimal Submanifolds .... 151
Exercises for Chapter 3 163
4. Geodesies and Jacobi Fields 165
4.1 1st and 2nd Variation of Arc Length and Energy 165
4.2 Jacobi Fields 172
4.3 Conjugate Points and Distance Minimizing Geodesies 180
4.4 Riemannian Manifolds of Constant Curvature 189
XII Contents
4.5 The Rauch Comparison Theorems and Other Jacobi Field
Estimates 190
4.6 Geometric Applications of Jacobi Field Estimates 196
4.7 Approximate Fundamental Solutions and Representation
Formulae 200
4.8 The Geometry of Manifolds of Nonpositive Sectional
Curvature 202
Exercises for Chapter 4 219
A Short Survey on Curvature and Topology 223
5. Symmetric Spaces and Kahler Manifolds 231
5.1 Complex Projective Space. Definition of Kahler Manifolds . 231
5.2 The Geometry of Symmetric Spaces 241
5.3 Some Results about the Structure of Symmetric Spaces .... 252
5.4 The Space Sl(n,R)/SO(n,R) 258
5.5 Symmetric Spaces of Noncompact Type as Examples of
Nonpositively Curved Riemannian Manifolds 275
Exercises for Chapter 5 279
6. Morse Theory and Floer Homology 281
6.1 Preliminaries: Aims of Morse Theory 281
6.2 Compactness: The Palais Smale Condition and the
Existence of Saddle Points 286
6.3 Local Analysis: Nondegeneracy of Critical Points, Morse ,
Lemma, Stable and Unstable Manifolds 289
6.4 Limits of Trajectories of the Gradient Flow 305
6.5 The Morse Smale Floer Condition: Transversality and !
Z2 Cohomology 312
6.6 Orientations and Z homology 318
6.7 Homotopies 323
6.8 Graph flows 327
6.9 Orientations 331
6.10 The Morse Inequalities 347
6.11 The Palais Smale Condition and the Existence of Closed
Geodesies 358
Exercises for Chapter 6 371
7. Variational Problems from Quantum Field Theory 373
7.1 The Ginzburg Landau Functional 373
7.2 The Seiberg Witten Functional 381
Exercises for Chapter 7 388
Contents XIII
8. Harmonic Maps 389
8.1 Definitions 389
8.2 Twodimensional Harmonic Mappings and Holomorphic
Quadratic Differentials 395
8.3 The Existence of Harmonic Maps in Two Dimensions 408
8.4 Definition and Lower Semicontinuity of the Energy
Integral 430
8.5 Weakly Harmonic Maps. Regularity Questions 441
8.6 Higher Regularity 456
8.7 Formulae for Harmonic Maps. The Bochner Technique .... 468
8.8 Harmonic Maps into Manifolds of Nonpositive Sectional
Curvature: Existence 480
8.9 Harmonic Maps into Manifolds of Nonpositive Sectional
Curvature: Regularity 486
8.10 Harmonic Maps into Manifolds of Nonpositive Sectional
Curvature: Uniqueness and Other properties 503
Exercises for Chapter 8 511
Appendix A: Linear Elliptic Partial Differential Equation ... 515
A.I Sobolev Spaces 515
A.2 Existence and Regularity Theory for Solutions
of Linear Elliptic Equations 519
Appendix B: Fundamental Groups and Covering Spaces .... 523
Index 527
|
| any_adam_object | 1 |
| author | Jost, Jürgen 1956- |
| author_GND | (DE-588)115774564 |
| author_facet | Jost, Jürgen 1956- |
| author_role | aut |
| author_sort | Jost, Jürgen 1956- |
| author_variant | j j jj |
| building | Verbundindex |
| bvnumber | BV013992790 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)248721645 (DE-599)BVBBV013992790 |
| 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 |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV013992790 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:43Z |
| institution | BVB |
| isbn | 3540426272 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009577902 |
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| physical | XIII, 532 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Jost, Jürgen 1956- Verfasser (DE-588)115774564 aut Riemannian geometry and geometric analysis Jürgen Jost 3. ed. Berlin [u.a.] Springer 2002 XIII, 532 S. txt rdacontent n rdamedia nc rdacarrier Universitext Geometrische Analysis Riemannsche Geometrie Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Geometrische Analysis (DE-588)4156708-0 s 1\p DE-604 DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009577902&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jost, Jürgen 1956- Riemannian geometry and geometric analysis Geometrische Analysis Riemannsche Geometrie Geometrische Analysis (DE-588)4156708-0 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4156708-0 (DE-588)4128462-8 |
| title | Riemannian geometry and geometric analysis |
| title_auth | Riemannian geometry and geometric analysis |
| title_exact_search | Riemannian geometry and geometric analysis |
| title_full | Riemannian geometry and geometric analysis Jürgen Jost |
| title_fullStr | Riemannian geometry and geometric analysis Jürgen Jost |
| title_full_unstemmed | Riemannian geometry and geometric analysis Jürgen Jost |
| title_short | Riemannian geometry and geometric analysis |
| title_sort | riemannian geometry and geometric analysis |
| topic | Geometrische Analysis Riemannsche Geometrie Geometrische Analysis (DE-588)4156708-0 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Geometrische Analysis Riemannsche Geometrie |
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