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OverviewThis 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. Full Product DetailsAuthor: D.N. KupeliPublisher: Springer Imprint: Springer Edition: Softcover reprint of hardcover 1st ed. 1996 Volume: 366 Dimensions: Width: 16.00cm , Height: 1.00cm , Length: 24.00cm Weight: 0.454kg ISBN: 9789048146895ISBN 10: 9048146895 Pages: 181 Publication Date: 05 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1 Preliminaries I: The Linear Algebra of Real Inner Product Spaces.- 2 A Review of Covariant Derivative Operators in Real Vector Bundles.- 3 Singular Semi-Riemannian Manifolds.- 4 Semi-Riemannian Submanifolds in Nondegenerate Semi-Riemannian Manifolds.- 5 Preliminaries II: Linear Algebra of Hermitian Inner Product Spaces.- 6 A Review of Covariant Derivative Operators in Complex Vector Bundles.- 7 Singular Kähler Manifolds.- 8 Hermitian Submanifolds of Nondegenerate 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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