Variational methods in Lorentzian geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Longman Scientific & Technical
1994
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
309 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 175 S. |
| ISBN: | 0582237998 |
Internformat
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| 245 | 1 | 0 | |a Variational methods in Lorentzian geometry |c Antonio Masiello |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Technical |c 1994 | |
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| 650 | 7 | |a Ongelijkheden |2 gtt | |
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| 650 | 4 | |a Critical point theory (Mathematical analysis) | |
| 650 | 4 | |a Geodesics (Mathematics) | |
| 650 | 4 | |a Morse theory | |
| 650 | 4 | |a Variational inequalities (Mathematics) | |
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Datensatz im Suchindex
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| adam_text | Contents
Introduction xiii
1. Semiriemannian manifolds 1
1.1 Scalar products 1
1.2 Minkowski products 3
1.3 Semiriemannian manifolds 4
1.4 Covariant Derivative 6
1.5 Parallel transport of vectors 9
1.6 Geodesies 12
1.7 Differential operators on a semiriemnnian manifold 14
1.8 Induced connection on a submanifold 18
1.9 Metric properties of Riemannian manifolds 21
2. Hilbert manifolds 24
2.1 Hilbert manifolds 24
2.2 Tangent space and smooth maps 25
2.3 Submanifolds 27
2.4 Riemannian manifolds 28
2.5 The Deformation Theorem 30
2.6 The Ljusternik Schnirelmann category 32
2.7 The Sobolev space # 2(7, Rn) 36
2.8 The Sobolev manifold H^ 2{I:M) 40
2.9 Approximations in Hh2(I, M) 42
2.10 Calculus in Hl 2(I,M) 48
2.11 Geodesies on Riemannian manifolds 52
3. Stationary Lorentzian manifolds 57
3.1 Introduction 57
3.2 Geodesies on stationary Lorentzian manifolds 59
ix
3.3 The variational principle 63
3.4 The geodesic connectedeness 66
3.5 Existence of timelike geodesies 68
4. Stationary Lorentzian manifolds with convex boundary 71
4.1 Semiriemannian manifolds with convex boundary 71
4.2 The penalization argument 73
4.3 A priori estimates for the critical points of the penalized functional 76
4.4 The geodesic connectedeness 80
4.5 Existence of timelike geodesies 85
5. A Morse Theory for geodesies on stationary Lorentzian manifolds 87
5.1 Introduction 87
5.2 The Hessian of a critical point 87
5.3 Abstract Morse Theory 89
5.4 The curvature tensor of a linear connection 93
5.5 The Hessian of a geodesic 94
5.6 The Hessian of a critical point of the functional J 97
5.7 Conjugate points along a geodesic 101
5.8 The second order variational principle 104
5.9 The Index Theorem 107
5.10 The Morse Relations: the case without boundary 112
5.11 The Morse Relations: the case with convex boundary 113
6. A Fermat principle for stationary Lorentzian manifolds 119
6.1 Introduction 119
6.2 The variational principle 119
6.3 Existence of lightlike geodesies 122
6.4 The Morse Relations for lightlike geodesies 125
6.5 Manifolds with light convex boundary 126
7. Applications 129
7.1 The Schwarzschild and Reissner Nordstrom space times 129
7.2 The Kerr space time I34
x
8. Geodesies on splitting manifolds 140
8.1 Introduction 140
8.2 The penalization argument 142
8.3 The Saddle Point Theorem 145
8.4 A priori estimates on the critical points of the penalized functional .... 151
8.5 The convexity of the boundary of a strip 157
8.6 The geodesic connectedeness 159
8.7 The Relative Category and the Serre Theorem for splitting manifolds . . 164
References 172
xi
|
| any_adam_object | 1 |
| author | Masiello, Antonio |
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| isbn | 0582237998 |
| language | English |
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| physical | XIX, 175 S. |
| publishDate | 1994 |
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| series | Pitman research notes in mathematics series |
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| spelling | Masiello, Antonio Verfasser aut Variational methods in Lorentzian geometry Antonio Masiello 1. publ. Harlow, Essex Longman Scientific & Technical 1994 XIX, 175 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 309 Geodeten gtt Géodésiques (Mathématiques) ram Inéquations variationnelles ram Kritisch punt gtt Morse theorie gtt Morse, théorie de ram Ongelijkheden gtt Point critique, théorie du (Analyse mathématique) ram Critical point theory (Mathematical analysis) Geodesics (Mathematics) Morse theory Variational inequalities (Mathematics) Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd rswk-swf Geodätische Linie (DE-588)4156669-5 gnd rswk-swf Lorentz-Mannigfaltigkeit (DE-588)4299989-3 s Geodätische Linie (DE-588)4156669-5 s DE-604 Pitman research notes in mathematics series 309 (DE-604)BV000022845 309 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006612258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Masiello, Antonio Variational methods in Lorentzian geometry Pitman research notes in mathematics series Geodeten gtt Géodésiques (Mathématiques) ram Inéquations variationnelles ram Kritisch punt gtt Morse theorie gtt Morse, théorie de ram Ongelijkheden gtt Point critique, théorie du (Analyse mathématique) ram Critical point theory (Mathematical analysis) Geodesics (Mathematics) Morse theory Variational inequalities (Mathematics) Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd Geodätische Linie (DE-588)4156669-5 gnd |
| subject_GND | (DE-588)4299989-3 (DE-588)4156669-5 |
| title | Variational methods in Lorentzian geometry |
| title_auth | Variational methods in Lorentzian geometry |
| title_exact_search | Variational methods in Lorentzian geometry |
| title_full | Variational methods in Lorentzian geometry Antonio Masiello |
| title_fullStr | Variational methods in Lorentzian geometry Antonio Masiello |
| title_full_unstemmed | Variational methods in Lorentzian geometry Antonio Masiello |
| title_short | Variational methods in Lorentzian geometry |
| title_sort | variational methods in lorentzian geometry |
| topic | Geodeten gtt Géodésiques (Mathématiques) ram Inéquations variationnelles ram Kritisch punt gtt Morse theorie gtt Morse, théorie de ram Ongelijkheden gtt Point critique, théorie du (Analyse mathématique) ram Critical point theory (Mathematical analysis) Geodesics (Mathematics) Morse theory Variational inequalities (Mathematics) Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd Geodätische Linie (DE-588)4156669-5 gnd |
| topic_facet | Geodeten Géodésiques (Mathématiques) Inéquations variationnelles Kritisch punt Morse theorie Morse, théorie de Ongelijkheden Point critique, théorie du (Analyse mathématique) Critical point theory (Mathematical analysis) Geodesics (Mathematics) Morse theory Variational inequalities (Mathematics) Lorentz-Mannigfaltigkeit Geodätische Linie |
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