Global Lorentzian geometry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1996
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
202 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 635 S. graph. Darst. |
| ISBN: | 0824793242 |
Staff View
MARC
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| 245 | 1 | 0 | |a Global Lorentzian geometry |c John K. Beem ; Paul E. Ehrlich ; Kevin L. Easley |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1996 | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface to the Second Edition iii
Preface to the First Edition vii
List of Figures xiii
1. Introduction: Riemannian Themes in Lorentzian Geometry 1
2. Connections and Curvature 15
2.1 Connections 16
2.2 Semi Riemannian Manifolds 20
2.3 Null Cones and Semi Riemannian Metrics 25
2.4 Sectional Curvature 29
2.5 The Generic Condition 33
2.6 The Einstein Equations 44
3. Lorentzian Manifolds and Causality 49
3.1 Lorentzian Manifolds and Convex Normal Neighborhoods 50
3.2 Causality Theory of Space times 54
3.3 Limit Curves and the C° Topology on Curves 72
3.4 Two Dimensional Space times 83
3.5 The Second Fundamental Form 92
3.6 Warped Products 94
3.7 Semi Riemannian Local Warped Product Splittings 117
ix
x CONTENTS
4. Lorentzian Distance 135
4.1 Basic Concepts and Definitions 135
4.2 Distance Preserving and Homothetic Maps 151
4.3 The Lorentzian Distance Function and Causality 157
4.4 Maximal Geodesic Segments and Local Causality 166
5. Examples of Space times 173
5.1 Minkowski Space time 174
5.2 Schwarzschild and Kerr Space times 179
5.3 Spaces of Constant Curvature 181
5.4 Robertson Walker Space times 185
5.5 Bi Invariant Lorentzian Metrics on Lie Groups 190
6. Completeness and Extendibility 197
6.1 Existence of Maximal Geodesic Segments 198
6.2 Geodesic Completeness 202
6.3 Metric Completeness 209
6.4 Ideal Boundaries 214
6.5 Local Extensions 219
6.6 Singularities 225
7. Stability of Completeness and Incompleteness 239
7.1 Stable Properties of Lor(M) and Con(M) 241
7.2 The C1 Topology and Geodesic Systems 247
7.3 Stability of Geodesic Incompleteness for Robertson Walker
Space times 250
7.4 Sufficient Conditions for Stability 263
8. Maximal Geodesies and Causally
Disconnected Space—times 271
8.1 Almost Maximal Curves and Maximal Geodesies 273
8.2 Nonspacelike Geodesic Rays in Strongly Causal Space times ... 279
8.3 Causally Disconnected Space times and Nonspacelike
Geodesic Lines 282
CONTENTS xi
9. The Lorentzian Cut Locus 295
9.1 The Timelike Cut Locus 298
9.2 The Null Cut Locus 305
9.3 The Nonspacelike Cut Locus 311
9.4 The Nonspacelike Cut Locus Revisited 318
10. Morse Index Theory on Lorentzian Manifolds 323
10.1 The Timelike Morse Index Theory 327
10.2 The Timelike Path Space of a Globally Hyperbolic
Space time 354
10.3 The Null Morse Index Theory 365
11. Some Results in Global Lorentzian Geometry 399
11.1 The Timelike Diameter 401
11.2 Lorentzian Comparison Theorems 406
11.3 Lorentzian Hadamard Cartan Theorems 411
12. Singularities 425
12.1 Jacobi Tensors 426
12.2 The Generic and Timelike Convergence Conditions 433
12.3 Focal Points 444
12.4 The Existence of Singularities 467
12.5 Smooth Boundaries 472
13. Gravitational Plane Wave Space times 479
13.1 The Metric, Geodesies, and Curvature 480
13.2 Astigmatic Conjugacy and the Nonspacelike Cut Locus 486
13.3 Astigmatic Conjugacy and the Achronal Boundary 493
14. The Splitting Problem in Global Lorentzian Geometry 501
14.1 The Busemann Function of a Timelike Geodesic Ray 507
14.2 Co rays and the Busemann Function 519
14.3 The Level Sets of the Busemann Function 538
14.4 The Proof of the Lorentzian Splitting Theorem 549
14.5 Rigidity of Geodesic Incompleteness 563
xii CONTENTS
Appendixes 567
A. Jacobi Fields and Toponogov s Theorem for Lorentzian
Manifolds by Steven G. Harris 567
B. From the Jacobi, to a Riccati, to the Raychaudhuri
Equation: Jacobi Tensor Fields and the Exponential Map
Revisited 573
References 587
List of Symbols 617
Index 623
|
| any_adam_object | 1 |
| author | Beem, John K. 1942- Ehrlich, Paul E. 1948- Easley, Kevin L. 1956- |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.37 |
| dewey-search | 516.37 |
| dewey-sort | 3516.37 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV010836183 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:59:44Z |
| institution | BVB |
| isbn | 0824793242 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007243123 |
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| physical | XIV, 635 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Beem, John K. 1942- Verfasser (DE-588)172001730 aut Global Lorentzian geometry John K. Beem ; Paul E. Ehrlich ; Kevin L. Easley 2. ed. New York [u.a.] Dekker 1996 XIV, 635 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 202 Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Relativitätstheorie (DE-588)4049363-5 s DE-604 Ehrlich, Paul E. 1948- Verfasser (DE-588)172067545 aut Easley, Kevin L. 1956- Verfasser (DE-588)172973384 aut Pure and applied mathematics 202 (DE-604)BV000001885 202 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007243123&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beem, John K. 1942- Ehrlich, Paul E. 1948- Easley, Kevin L. 1956- Global Lorentzian geometry Pure and applied mathematics Relativitätstheorie (DE-588)4049363-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4049363-5 (DE-588)4012248-7 |
| title | Global Lorentzian geometry |
| title_auth | Global Lorentzian geometry |
| title_exact_search | Global Lorentzian geometry |
| title_full | Global Lorentzian geometry John K. Beem ; Paul E. Ehrlich ; Kevin L. Easley |
| title_fullStr | Global Lorentzian geometry John K. Beem ; Paul E. Ehrlich ; Kevin L. Easley |
| title_full_unstemmed | Global Lorentzian geometry John K. Beem ; Paul E. Ehrlich ; Kevin L. Easley |
| title_short | Global Lorentzian geometry |
| title_sort | global lorentzian geometry |
| topic | Relativitätstheorie (DE-588)4049363-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Relativitätstheorie Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007243123&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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