Osserman manifolds in semi-Riemannian geometry:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
|
| Series: | Lecture notes in mathematics
1777 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 166 S. |
| ISBN: | 3540431446 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1. The Osserman Conditions in Semi Riemannian Geometry 1
1.1 The Jacobi Operator 1
1.2 The Timelike and Spacelike Osserman Conditions at a Point . 3
1.3 Semi Riemannian Pointwise and Global Osserman Manifolds . 9
2. The Osserman Conjecture in Riemannian Geometry 21
2.1 Partial Solution to the Osserman Conjecture 22
2.1.1 Odd Dimensional Riemannian Pointwise Osserman Man¬
ifolds 22
2.1.2 (4m + 2) Dimensional Riemannian Pointwise Osser¬
man Manifolds 23
2.1.3 Four Dimensional Riemannian Osserman Manifolds ... 29
2.2 A Solution to the Osserman Conjecture with Additional As¬
sumptions 31
2.2.1 Kahler and Quaternionic Kahler Manifolds 31
2.2.2 Riemannian Osserman Manifolds with Two Distinct
Eigenvalues 34
2.2.3 Homogeneous Manifolds of Negative Sectional Curvature 35
3. Lorentzian Osserman Manifolds 39
3.1 The Complete Solution to the Osserman Problem 39
3.2 The Null Osserman Condition 44
3.2.1 The Null Osserman Condition at a Point 46
3.2.2 Decomposition Theorems 53
4. Four Dimensional Semi Riemannian Osserman Manifolds
with Metric Tensors of Signature (2, 2) 63
4.1 Nonsymmetric Semi Riemannian Osserman Manifolds with
Metric Tensors of Signature (2,2) 64
4.2 Semi Riemannian Osserman and Jordan Osserman Manifolds
with Metric Tensors of Signature (2,2) 70
4.2.1 Osserman Algebraic Curvature Tensors on Four Dimensional
Vector Spaces of Neutral Signature 70
XII Contents
4.2.2 Four Dimensional Semi Riemannian Pointwise Osser
man Manifolds 79
4.2.3 Symmetric Semi Riemannian Osserman Manifolds with
Metric Tensors of Signature (2,2) 84
4.2.4 Classification of Semi Riemannian Jordan Osserman
Manifolds with Metric Tensors of Signature (2,2) 90
5. Semi Riemannian Osserman Manifolds 95
5.1 Nonsymmetric Semi Riemannian Osserman Manifolds of Ar¬
bitrary Signature 95
5.1.1 Indefinite Kahler Osserman Manifolds 96
5.1.2 Semi Riemannian Osserman Metric Tensors on Tan¬
gent Bundles 99
5.2 Special Semi Riemannian Osserman Manifolds 102
5.3 Classification of Semi Riemannian Special Osserman Manifoldsl04
5.3.1 Multiplicities of the Eigenvalues 113
5.3.2 Semi Riemannian Special Osserman Manifolds of Di¬
mensions Different from 16 and 32 119
5.3.3 Semi Riemannian Special Osserman Manifolds of Di¬
mensions 16 and 32 129
6. Generalizations and Osserman Related Conditions 137
6.1 Semi Riemannian Generalized Osserman Manifolds 137
6.2 The Osserman Condition in Affine Differential Geometry .... 143
6.2.1 Affine Osserman Manifolds 143
6.2.2 Semi Riemannian Osserman Metric Tensors on Cotan¬
gent Bundles 146
6.3 Riemannian Manifolds with Isoparametric Geodesic Spheres . 150
6.4 Riemannian C manifolds 151
6.5 Skew Symmetric Curvature Operators 152
6.5.1 Riemannian Manifolds whose Skew Symmetric Curva¬
ture Operators Have Constant Eigenvalues along each
Circle 155
References 157
Index 165
|
| any_adam_object | 1 |
| author | García-Río, Eduardo 1965- Kupeli, Demir N. Vázquez-Lorenzo, Ramón 1971- |
| author_GND | (DE-588)123438357 (DE-588)123438322 |
| author_facet | García-Río, Eduardo 1965- Kupeli, Demir N. Vázquez-Lorenzo, Ramón 1971- |
| author_role | aut aut aut |
| author_sort | García-Río, Eduardo 1965- |
| author_variant | e g r egr d n k dn dnk r v l rvl |
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| discipline | Mathematik |
| format | Book |
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| physical | XII, 166 S. |
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| series2 | Lecture notes in mathematics |
| spelling | García-Río, Eduardo 1965- Verfasser (DE-588)123438357 aut Osserman manifolds in semi-Riemannian geometry Eduardo García-Río ; Demir N. Kupeli ; Ramón Vázquez-Lorenzo Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 XII, 166 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1777 Globale Differentialgeometrie - Pseudo-Riemannscher Raum Geometry, Riemannian Riemannian manifolds Globale Differentialgeometrie (DE-588)4021286-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd rswk-swf Globale Differentialgeometrie (DE-588)4021286-5 s Pseudo-Riemannscher Raum (DE-588)4176163-7 s DE-604 Riemannscher Raum (DE-588)4128295-4 s Lorentz-Mannigfaltigkeit (DE-588)4299989-3 s Mathematische Physik (DE-588)4037952-8 s Kupeli, Demir N. Verfasser aut Vázquez-Lorenzo, Ramón 1971- Verfasser (DE-588)123438322 aut Lecture notes in mathematics 1777 (DE-604)BV000676446 1777 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009683292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | García-Río, Eduardo 1965- Kupeli, Demir N. Vázquez-Lorenzo, Ramón 1971- Osserman manifolds in semi-Riemannian geometry Lecture notes in mathematics Globale Differentialgeometrie - Pseudo-Riemannscher Raum Geometry, Riemannian Riemannian manifolds Globale Differentialgeometrie (DE-588)4021286-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd Riemannscher Raum (DE-588)4128295-4 gnd Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd |
| subject_GND | (DE-588)4021286-5 (DE-588)4037952-8 (DE-588)4176163-7 (DE-588)4128295-4 (DE-588)4299989-3 |
| title | Osserman manifolds in semi-Riemannian geometry |
| title_auth | Osserman manifolds in semi-Riemannian geometry |
| title_exact_search | Osserman manifolds in semi-Riemannian geometry |
| title_full | Osserman manifolds in semi-Riemannian geometry Eduardo García-Río ; Demir N. Kupeli ; Ramón Vázquez-Lorenzo |
| title_fullStr | Osserman manifolds in semi-Riemannian geometry Eduardo García-Río ; Demir N. Kupeli ; Ramón Vázquez-Lorenzo |
| title_full_unstemmed | Osserman manifolds in semi-Riemannian geometry Eduardo García-Río ; Demir N. Kupeli ; Ramón Vázquez-Lorenzo |
| title_short | Osserman manifolds in semi-Riemannian geometry |
| title_sort | osserman manifolds in semi riemannian geometry |
| topic | Globale Differentialgeometrie - Pseudo-Riemannscher Raum Geometry, Riemannian Riemannian manifolds Globale Differentialgeometrie (DE-588)4021286-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd Riemannscher Raum (DE-588)4128295-4 gnd Lorentz-Mannigfaltigkeit (DE-588)4299989-3 gnd |
| topic_facet | Globale Differentialgeometrie - Pseudo-Riemannscher Raum Geometry, Riemannian Riemannian manifolds Globale Differentialgeometrie Mathematische Physik Pseudo-Riemannscher Raum Riemannscher Raum Lorentz-Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009683292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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