Singular Semi-Riemannian Geometry by D.N. KupeliSingular Semi-Riemannian Geometry by D.N. Kupeli

Singular Semi-Riemannian Geometry

byD.N. Kupeli

Paperback | December 5, 2010

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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 Kähler manifolds in four chapters parallel to Part I. Finally, Part III consists of three chapters treating singular quaternionic Kähler manifolds. Audience: 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.
Title:Singular Semi-Riemannian GeometryFormat:PaperbackDimensions:191 pages, 9.45 × 6.3 × 0 inPublished:December 5, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048146895

ISBN - 13:9789048146895

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Table of Contents

Preface. I: Singular Semi-Riemannian Manifolds. 1. Preliminaries I: The Linear Algebra of Real Inner Product Spaces. 2. A Review of Covariant Derivative Operators in Real Vector Bundels. 3. Singular Semi-Riemannian Manifolds. 4. Semi-Riemannian Submanifolds in Nondegenerate Semi-Riemannian Manifolds. II: Singular Kähler Manifolds. 5. Preliminaries II: Linear Algebra of Hermitian Inner Product Spaces. 6. A Review of Covariant Derivative Operators on Complex Vector Bundles. 7. Singular Kähler Manifolds. 8. Hermitian Submanifolds of Nondegenerate Kähler Manifolds. III: Singular Quaternionic Kähler Manifolds. 9. Preliminaries III: Linear Algebra of Quaternionic Inner Product Spaces. 10. Singular Quaternionic Kähler Manifolds. 11. Quaternionic Semi-Riemannian Submanifolds of Nondegenerate Quaternionic Kähler Manifolds. References. Index.