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Mathematics and Its Applications

Singular Semi-Riemannian Geometry

Authors: Kupeli, D.N.

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eBook 96,29 €
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  • ISBN 978-94-015-8761-7
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Hardcover 119,99 €
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  • ISBN 978-0-7923-3996-0
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Softcover 119,99 €
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  • ISBN 978-90-481-4689-5
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About this book

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 96,29 €
price for India (gross)
  • ISBN 978-94-015-8761-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 119,99 €
price for India (gross)
  • ISBN 978-0-7923-3996-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover 119,99 €
price for India (gross)
  • ISBN 978-90-481-4689-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Singular Semi-Riemannian Geometry
Authors
Series Title
Mathematics and Its Applications
Series Volume
366
Copyright
1996
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-8761-7
DOI
10.1007/978-94-015-8761-7
Hardcover ISBN
978-0-7923-3996-0
Softcover ISBN
978-90-481-4689-5
Edition Number
1
Number of Pages
X, 181
Topics