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."
General
| Imprint: |
Springer
|
| Country of origin: |
Netherlands |
| Series: |
Mathematics and Its Applications, 366 |
| Release date: |
December 2010 |
| First published: |
1996 |
| Authors: |
D.N. Kupeli
|
| Dimensions: |
240 x 160 x 10mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
181 |
| Edition: |
Softcover reprint of hardcover 1st ed. 1996 |
| ISBN-13: |
978-90-481-4689-5 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Differential & Riemannian geometry
|
| LSN: |
90-481-4689-5 |
| Barcode: |
9789048146895 |
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