Singular Semi-Riemannian Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
366 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an exposition of "Singular Semi-Riemannian Geometry"- 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 the metric tensor is assumed to be nondegenerate. In the literature, manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi Riemannian manifolds. One major aspect of this book is first to study the intrinsic structure of a manifold with a degenerate metric tensor and then to study it extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. This book is divided into three parts. Part I deals with singular semi Riemannian manifolds in four chapters. In Chapter I, the linear algebra of indefinite real inner product spaces is reviewed. In general, properties of certain geometric tensor fields are obtained purely from the algebraic point of view without referring to their geometric origin. Chapter II is devoted to a review of covariant derivative operators in real vector bundles. Chapter III is the main part of this book where, intrinsically, the Koszul connection is introduced and its curvature identities are obtained. In Chapter IV, an application of Chapter III is made to degenerate submanifolds of semi-Riemannian manifolds and Gauss, Codazzi and Ricci equations are obtained. Part II deals with singular Kahler manifolds in four chapters parallel to Part I. |
| Beschreibung: | 1 Online-Ressource (X, 181 p) |
| ISBN: | 9789401587617 9789048146895 |
| DOI: | 10.1007/978-94-015-8761-7 |
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Datensatz im Suchindex
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| author | Kupeli, Demir N. |
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| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8761-7 |
| format | Electronic eBook |
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| id | DE-604.BV042424087 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401587617 9789048146895 |
| language | English |
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| physical | 1 Online-Ressource (X, 181 p) |
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| spelling | Kupeli, Demir N. Verfasser aut Singular Semi-Riemannian Geometry by Demir N. Kupeli Dordrecht Springer Netherlands 1996 1 Online-Ressource (X, 181 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 366 This book is an exposition of "Singular Semi-Riemannian Geometry"- 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 the metric tensor is assumed to be nondegenerate. In the literature, manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi Riemannian manifolds. One major aspect of this book is first to study the intrinsic structure of a manifold with a degenerate metric tensor and then to study it extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. This book is divided into three parts. Part I deals with singular semi Riemannian manifolds in four chapters. In Chapter I, the linear algebra of indefinite real inner product spaces is reviewed. In general, properties of certain geometric tensor fields are obtained purely from the algebraic point of view without referring to their geometric origin. Chapter II is devoted to a review of covariant derivative operators in real vector bundles. Chapter III is the main part of this book where, intrinsically, the Koszul connection is introduced and its curvature identities are obtained. In Chapter IV, an application of Chapter III is made to degenerate submanifolds of semi-Riemannian manifolds and Gauss, Codazzi and Ricci equations are obtained. Part II deals with singular Kahler manifolds in four chapters parallel to Part I. Mathematics Global differential geometry Differential Geometry Mathematik 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 1\p DE-604 https://doi.org/10.1007/978-94-015-8761-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kupeli, Demir N. Singular Semi-Riemannian Geometry Mathematics Global differential geometry Differential Geometry Mathematik 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 | Mathematics Global differential geometry Differential Geometry Mathematik Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Mathematics Global differential geometry Differential Geometry Mathematik Glatte Mannigfaltigkeit Tensorrechnung |
| url | https://doi.org/10.1007/978-94-015-8761-7 |
| work_keys_str_mv | AT kupelidemirn singularsemiriemanniangeometry |