Singular semi-Riemannian geometry:
This volume is an exposition of singular semi-Riemannian geometry, i.e. the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where metric tensors are assumed to be nondegenerate. In the literature manifo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Mathematics and its applications
366 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This volume is an exposition of singular semi-Riemannian geometry, i.e. the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where metric tensors are assumed to be nondegenerate. In the literature manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi-Riemannian manifolds. Here, the intrinsic structure of a manifold with a degenerate metric tensor is studied first, and then it is studied extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. The book is divided into three parts. The four chapters of Part I deal with singular semi-Riemannian manifolds. Part II is concerned with singular Kahler manifolds in four chapters parallel to Part I. Finally, Part III consists of three chapters treating singular quaternionic Kahler manifolds This self-contained book will be of interest to graduate students of differential geometry, who have some background knowledge on the subject of complex manifolds already |
| Physical Description: | X, 177 S. |
| ISBN: | 0792339967 |
Staff View
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| 520 | 3 | |a This volume is an exposition of singular semi-Riemannian geometry, i.e. the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where metric tensors are assumed to be nondegenerate. In the literature manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi-Riemannian manifolds. Here, the intrinsic structure of a manifold with a degenerate metric tensor is studied first, and then it is studied extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. The book is divided into three parts. The four chapters of Part I deal with singular semi-Riemannian manifolds. Part II is concerned with singular Kahler manifolds in four chapters parallel to Part I. Finally, Part III consists of three chapters treating singular quaternionic Kahler manifolds | |
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Record in the Search Index
| _version_ | 1804125352291729408 |
|---|---|
| adam_text | Table of Contents
Preface ix
I Singular Semi Riemannian Manifolds 1
1 Preliminaries I: The Linear Algebra of Real Inner
Product Spaces 3
1.1 Real Inner Product Spaces 3
1.2 Subspaces of Nondegenerate Inner Product Spaces 5
1.3 Nondegenerate Quotient Spaces 7
1.4 Bilinear Forms on Nondegenerate Inner Product Spaces . . 8
1.5 Curvaturelike Quadrilinear Functions on Nondegenerate
Real Inner Product Spaces 10
2 A Review of Covariant Derivative Operators in
Real Vector Bundles 23
2.1 Covariant Derivative Operators 23
2.2 Curvature Tensor 26
2.3 Semi Riemannian Covariant Derivative Operators 28
2.4 The Pullback Covariant Derivative Operators 30
2.5 Terminology 37
3 Singular Semi Riemannian Manifolds 39
3.1 Koszul Derivatives 39
3.2 The Koszul Connection 46
3.3 Curvatures of Stationary Semi Riemannian Manifolds ... 50
3.4 Fibration of Semi Riemannian Manifolds 54
4 Semi Riemannian Submanifolds in Nondegenerate
Semi Riemannian Manifolds 61
4.1 Integrable, Irrotational and Stationary
Semi Riemannian Submanifolds 61
v
vi TABLE OF CONTENTS
4.2 Second Fundamental Form Tensors 65
4.3 Gauss, Codazzi and Ricci Equations 72
4.4 Umbilic Semi Riemannian Submanifolds 80
4.5 Deviation of Null Generators 83
II Singular Kahler Manifolds 89
5 Preliminaries II: Linear Algebra of Hermitian
Inner Product Spaces 91
5.1 Complex Vector Spaces 91
5.2 Hermitian Inner Product Spaces 93
5.3 Holomorphic Curvaturelike Quadrilinear Functions on
Nondegenerate Hermitian Inner Product Spaces 94
6 A Review of Covariant Derivative Operators in
Complex Vector Bundles 111
6.1 Connections in Hermitian Vector Bundles Ill
6.2 Connections in Hermitian Holomorphic Vector Bundles ... 115
7 Singular Kahler Manifolds 119
7.1 Kahler Manifolds 119
7.2 Curvatures of Kahler Manifolds 124
7.3 Complex Kahler Manifolds 128
8 Hermitian Submanifolds of Nondegenerate
Kahler Manifolds 133
8.1 Second Fundamental Form Tensor of
Hermitian Submanifolds 133
8.2 Totally Geodesic Hermitian Submanifolds of Nondegenerate
Kahler Manifolds 136
III Singular Quaternionic Kahler Manifolds 141
9 Preliminaries III: Linear Algebra of Quaternionic
Inner Product Spaces 143
9.1 Quaternionic Inner Product Spaces 143
9.2 Quaternionic Curvaturelike Quadrilinear Functions on
Nondegenerate Quaternionic Inner Product Spaces 144
Singular Semi Riemannian Geometry vii
10 Singular Quaternionic Kahler Manifolds 163
10.1 Quaternionic Kahler Manifolds 163
10.2 Curvatures of Quaternionic Kahler Manifolds 166
11 Quaternionic Semi Riemannian Submanifolds of
Nondegenerate Quaternionic Kahler Manifolds 171
11.1 Quaternionic Semi Riemannian Submanifolds 171
References 173
Index 174
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:00:12Z |
| institution | BVB |
| isbn | 0792339967 |
| language | English |
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| physical | X, 177 S. |
| publishDate | 1996 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
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| spelling | Kupeli, Demir N. Verfasser aut Singular semi-Riemannian geometry by Demir N. Kupeli Dordrecht [u.a.] Kluwer 1996 X, 177 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 366 This volume is an exposition of singular semi-Riemannian geometry, i.e. the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where metric tensors are assumed to be nondegenerate. In the literature manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi-Riemannian manifolds. Here, the intrinsic structure of a manifold with a degenerate metric tensor is studied first, and then it is studied extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. The book is divided into three parts. The four chapters of Part I deal with singular semi-Riemannian manifolds. Part II is concerned with singular Kahler manifolds in four chapters parallel to Part I. Finally, Part III consists of three chapters treating singular quaternionic Kahler manifolds This self-contained book will be of interest to graduate students of differential geometry, who have some background knowledge on the subject of complex manifolds already Riemann, Géométrie de ram Semi-Riemannian geometry Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Glatte Mannigfaltigkeit (DE-588)4157471-0 s Tensorrechnung (DE-588)4192487-3 s DE-604 Mathematics and its applications 366 (DE-604)BV008163334 366 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007262738&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kupeli, Demir N. Singular semi-Riemannian geometry Mathematics and its applications Riemann, Géométrie de ram Semi-Riemannian geometry Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4157471-0 (DE-588)4192487-3 |
| title | Singular semi-Riemannian geometry |
| title_auth | Singular semi-Riemannian geometry |
| title_exact_search | Singular semi-Riemannian geometry |
| title_full | Singular semi-Riemannian geometry by Demir N. Kupeli |
| title_fullStr | Singular semi-Riemannian geometry by Demir N. Kupeli |
| title_full_unstemmed | Singular semi-Riemannian geometry by Demir N. Kupeli |
| title_short | Singular semi-Riemannian geometry |
| title_sort | singular semi riemannian geometry |
| topic | Riemann, Géométrie de ram Semi-Riemannian geometry Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Riemann, Géométrie de Semi-Riemannian geometry Glatte Mannigfaltigkeit Tensorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007262738&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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