| Singular Semi-Riemannian Geometry 1996 Edition Contributor(s): Kupeli, D. N. (Author) |
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ISBN: 0792339967 ISBN-13: 9780792339960 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: April 1996 Annotation: 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 K?hler manifolds in four chapters parallel to Part I. Finally, Part III consists of three chapters treating singular quaternionic K?hler 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Geometry - Analytic |
| Dewey: 516.373 |
| LCCN: 96010934 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.5" H x 6.14" W x 9.21" (1.00 lbs) 181 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |