Singular Semi Riemannian Geometry

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Singular Semi Riemannian Geometry

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Author : D. N. Kupeli
language : en
Publisher:
Release Date : 2014-01-15

Singular Semi Riemannian Geometry written by D. N. Kupeli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Mat Report

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Author :
language : en
Publisher:
Release Date : 1990

Mat Report written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Singular Semi Riemannian Geometry

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Author : Jens Chr Larsen
language : en
Publisher:
Release Date : 1990

Singular Semi Riemannian Geometry written by Jens Chr Larsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Singular Semi Riemannian Geometry

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Author : D.N. Kupeli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Singular Semi Riemannian Geometry written by D.N. Kupeli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

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.

Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds. The growing importance of light like hypersurfaces in mathematical physics, in particular their extensive use in relativity, and very limited information available on the general theory of lightlike submanifolds, motivated the present authors, in 1990, to do collaborative research on the subject matter of this book. Based on a series of author's papers (Bejancu [3], Bejancu-Duggal [1,3], Dug gal [13], Duggal-Bejancu [1,2,3]) and several other researchers, this volume was conceived and developed during the Fall '91 and Fall '94 visits of Bejancu to the University of Windsor, Canada. The primary difference between the lightlike submanifold and that of its non degenerate counterpart arises due to the fact that in the first case, the normal vector bundle intersects with the tangent bundle of the submanifold. Thus, one fails to use, in the usual way, the theory of non-degenerate submanifolds (cf. Chen [1]) to define the induced geometric objects (such as linear connection, second fundamental form, Gauss and Weingarten equations) on the light like submanifold. Some work is known on null hypersurfaces and degenerate submanifolds (see an up-to-date list of references on pages 138 and 140 respectively). Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of an up-to-date information on null curves, lightlike hypersur faces and submanifolds, consistent with the theory of non-degenerate submanifolds.

Singular Semi Riemannian Geometry

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Author : D.N. Kupeli
language : en
Publisher: Springer
Release Date : 2010-12-05

Singular Semi Riemannian Geometry written by D.N. Kupeli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-05 with Mathematics categories.

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.

Osserman Manifolds In Semi Riemannian Geometry

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Author : Eduardo Garcia-Rio
language : en
Publisher: Springer
Release Date : 2004-10-12

Osserman Manifolds In Semi Riemannian Geometry written by Eduardo Garcia-Rio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-12 with Mathematics categories.

The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

Symmetries Of Spacetimes And Riemannian Manifolds

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Symmetries Of Spacetimes And Riemannian Manifolds written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.

This book provides an upto date information on metric, connection and curva ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of a comprehensive collection of the works of a very large number of researchers on all the above mentioned symmetries. (b) We have aimed at bringing together the researchers interested in differential geometry and the mathematical physics of general relativity by giving an invariant as well as the index form of the main formulas and results. (c) Attempt has been made to support several main mathematical results by citing physical example(s) as applied to general relativity. (d) Overall the presentation is self contained, fairly accessible and in some special cases supported by an extensive list of cited references. (e) The material covered should stimulate future research on symmetries. Chapters 1 and 2 contain most of the prerequisites for reading the rest of the book. We present the language of semi-Euclidean spaces, manifolds, their tensor calculus; geometry of null curves, non-degenerate and degenerate (light like) hypersurfaces. All this is described in invariant as well as the index form.

New Developments In Differential Geometry Budapest 1996

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Author : J. Szenthe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

New Developments In Differential Geometry Budapest 1996 written by J. Szenthe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Differential Geometry Of Lightlike Submanifolds

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02

Differential Geometry Of Lightlike Submanifolds written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Mathematics categories.

This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.