Singular Semi-Riemannian Geometry

ISBN-13: 9789048146895 / Angielski / Miękka / 2010 / 181 str.

D. N. Kupeli

Opis

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. 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.

Spis treści

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.