Semi Riemannian Geometry

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Semi-Riemannian Geometry With Applications to Relativity

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Author : Barrett O'Neill
Publisher : Academic Press
ISBN 13 : 0080570577
Total Pages : 483 pages
Book Rating : 4.0/5 (85 download)

Book Synopsis Semi-Riemannian Geometry With Applications to Relativity by : Barrett O'Neill

Download or read book Semi-Riemannian Geometry With Applications to Relativity written by Barrett O'Neill and published by Academic Press. This book was released on 1983-07-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Semi-Riemannian Geometry

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Author : Stephen C. Newman
Publisher : John Wiley & Sons
ISBN 13 : 1119517532
Total Pages : 656 pages
Book Rating : 4.1/5 (195 download)

Book Synopsis Semi-Riemannian Geometry by : Stephen C. Newman

Download or read book Semi-Riemannian Geometry written by Stephen C. Newman and published by John Wiley & Sons. This book was released on 2019-07-30 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.

Singular Semi-Riemannian Geometry

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Author : D.N. Kupeli
Publisher : Springer
ISBN 13 : 9789048146895
Total Pages : 0 pages
Book Rating : 4.1/5 (468 download)

Book Synopsis Singular Semi-Riemannian Geometry by : D.N. Kupeli

Download or read book Singular Semi-Riemannian Geometry written by D.N. Kupeli and published by Springer. This book was released on 2010-12-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3540456295
Total Pages : 170 pages
Book Rating : 4.5/5 (44 download)

Book Synopsis Osserman Manifolds in Semi-Riemannian Geometry by : Eduardo Garcia-Rio

Download or read book Osserman Manifolds in Semi-Riemannian Geometry written by Eduardo Garcia-Rio and published by Springer. This book was released on 2004-10-14 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

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Author : Krishan L. Duggal
Publisher : Springer Science & Business Media
ISBN 13 : 9401720894
Total Pages : 311 pages
Book Rating : 4.4/5 (17 download)

Book Synopsis Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications by : Krishan L. Duggal

Download or read book Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Curvature in Mathematics and Physics

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Author : Shlomo Sternberg
Publisher : Courier Corporation
ISBN 13 : 0486292711
Total Pages : 416 pages
Book Rating : 4.4/5 (862 download)

Book Synopsis Curvature in Mathematics and Physics by : Shlomo Sternberg

Download or read book Curvature in Mathematics and Physics written by Shlomo Sternberg and published by Courier Corporation. This book was released on 2013-04-17 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Introduction to Riemannian Manifolds

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Author : John M. Lee
Publisher : Springer
ISBN 13 : 3319917552
Total Pages : 437 pages
Book Rating : 4.3/5 (199 download)

Book Synopsis Introduction to Riemannian Manifolds by : John M. Lee

Download or read book Introduction to Riemannian Manifolds written by John M. Lee and published by Springer. This book was released on 2019-01-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

An Introduction to Riemannian Geometry

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Author : Leonor Godinho
Publisher : Springer
ISBN 13 : 3319086669
Total Pages : 476 pages
Book Rating : 4.3/5 (19 download)

Book Synopsis An Introduction to Riemannian Geometry by : Leonor Godinho

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Differential Geometry Of Warped Product Manifolds And Submanifolds

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Author : Chen Bang-yen
Publisher : World Scientific
ISBN 13 : 9813208945
Total Pages : 516 pages
Book Rating : 4.8/5 (132 download)

Book Synopsis Differential Geometry Of Warped Product Manifolds And Submanifolds by : Chen Bang-yen

Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Chen Bang-yen and published by World Scientific. This book was released on 2017-05-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson–Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson–Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.

Comparison Theorems in Riemannian Geometry

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Author : Jeff Cheeger
Publisher : Newnes
ISBN 13 : 0444107649
Total Pages : 183 pages
Book Rating : 4.4/5 (441 download)

Book Synopsis Comparison Theorems in Riemannian Geometry by : Jeff Cheeger

Download or read book Comparison Theorems in Riemannian Geometry written by Jeff Cheeger and published by Newnes. This book was released on 2009-01-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comparison Theorems in Riemannian Geometry

Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

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Author : Krishan L Duggal
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106972
Total Pages : 304 pages
Book Rating : 4.8/5 (131 download)

Book Synopsis Null Curves and Hypersurfaces of Semi-Riemannian Manifolds by : Krishan L Duggal

Download or read book Null Curves and Hypersurfaces of Semi-Riemannian Manifolds written by Krishan L Duggal and published by World Scientific Publishing Company. This book was released on 2007-09-03 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: A systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering.The geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.

Spacetime

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Author : Marcus Kriele
Publisher : Springer Science & Business Media
ISBN 13 : 3540483543
Total Pages : 436 pages
Book Rating : 4.5/5 (44 download)

Book Synopsis Spacetime by : Marcus Kriele

Download or read book Spacetime written by Marcus Kriele and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Manifolds and Differential Geometry

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Author : Jeffrey M. Lee
Publisher : American Mathematical Society
ISBN 13 : 1470469820
Total Pages : 671 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Manifolds and Differential Geometry by : Jeffrey M. Lee

Download or read book Manifolds and Differential Geometry written by Jeffrey M. Lee and published by American Mathematical Society. This book was released on 2022-03-08 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.

Pseudo-Riemannian Geometry, [delta]-invariants and Applications

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Author : Bang-yen Chen
Publisher : World Scientific
ISBN 13 : 9814329649
Total Pages : 510 pages
Book Rating : 4.8/5 (143 download)

Book Synopsis Pseudo-Riemannian Geometry, [delta]-invariants and Applications by : Bang-yen Chen

Download or read book Pseudo-Riemannian Geometry, [delta]-invariants and Applications written by Bang-yen Chen and published by World Scientific. This book was released on 2011 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold

Modern Differential Geometry for Physicists

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Author : Chris J. Isham
Publisher : Allied Publishers
ISBN 13 : 9788177643169
Total Pages : 308 pages
Book Rating : 4.6/5 (431 download)

Book Synopsis Modern Differential Geometry for Physicists by : Chris J. Isham

Download or read book Modern Differential Geometry for Physicists written by Chris J. Isham and published by Allied Publishers. This book was released on 2002 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Riemannian Manifolds

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Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387227261
Total Pages : 232 pages
Book Rating : 4.3/5 (872 download)

Book Synopsis Riemannian Manifolds by : John M. Lee

Download or read book Riemannian Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Isometric Embeddings of Riemannian and Pseudo-Riemannian Manifolds

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Author : Robert Everist Greene
Publisher : American Mathematical Soc.
ISBN 13 : 0821812971
Total Pages : 69 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Isometric Embeddings of Riemannian and Pseudo-Riemannian Manifolds by : Robert Everist Greene

Download or read book Isometric Embeddings of Riemannian and Pseudo-Riemannian Manifolds written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1970 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: