Symmetries Of Spacetimes And Riemannian Manifolds

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Symmetries of Spacetimes and Riemannian Manifolds

Author : Krishan L. Duggal
Publisher : Springer Science & Business Media
ISBN 13 : 1461553156
Total Pages : 227 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Symmetries of Spacetimes and Riemannian Manifolds by : Krishan L. Duggal

Download or read book Symmetries of Spacetimes and Riemannian Manifolds written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symmetries of Spacetimes and Riemannian Manifolds

Author : Krishan Duggal
Publisher :
ISBN 13 : 9781461553168
Total Pages : 232 pages
Book Rating : 4.5/5 (531 download)

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Book Synopsis Symmetries of Spacetimes and Riemannian Manifolds by : Krishan Duggal

Download or read book Symmetries of Spacetimes and Riemannian Manifolds written by Krishan Duggal and published by . This book was released on 2014-09-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

Author : Krishan L. Duggal
Publisher : World Scientific
ISBN 13 : 981270647X
Total Pages : 302 pages
Book Rating : 4.8/5 (127 download)

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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. This book was released on 2007 with total page 302 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.

Recent Developments in Pseudo-Riemannian Geometry

Author : Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher : European Mathematical Society
ISBN 13 : 9783037190517
Total Pages : 556 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Recent Developments in Pseudo-Riemannian Geometry by : Dmitriĭ Vladimirovich Alekseevskiĭ

Download or read book Recent Developments in Pseudo-Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and published by European Mathematical Society. This book was released on 2008 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.

Spacetime

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

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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.

Handbook of Differential Geometry

Author : Franki J.E. Dillen
Publisher : Elsevier
ISBN 13 : 9780080461205
Total Pages : 574 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Handbook of Differential Geometry by : Franki J.E. Dillen

Download or read book Handbook of Differential Geometry written by Franki J.E. Dillen and published by Elsevier. This book was released on 2005-11-29 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Hermitian–Grassmannian Submanifolds

Author : Young Jin Suh
Publisher : Springer
ISBN 13 : 9811055564
Total Pages : 360 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Hermitian–Grassmannian Submanifolds by : Young Jin Suh

Download or read book Hermitian–Grassmannian Submanifolds written by Young Jin Suh and published by Springer. This book was released on 2017-09-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016. The Workshop was supported by the Research Institute of Real and Complex Manifolds (RIRCM) and the National Research Foundation of Korea (NRF). The Organizing Committee invited 30 active geometers of differential geometry and related fields from all around the globe to discuss new developments for research in the area. These proceedings provide a detailed overview of recent topics in the field of real and complex submanifolds.

Advances in Differential Geometry and General Relativity

Author : John K. Beem
Publisher : American Mathematical Soc.
ISBN 13 : 0821835394
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advances in Differential Geometry and General Relativity by : John K. Beem

Download or read book Advances in Differential Geometry and General Relativity written by John K. Beem and published by American Mathematical Soc.. This book was released on 2004 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of expanded versions of invited lectures given at The Beemfest: Advances in Differential Geometry and General Relativity (University of Missouri-Columbia) on the occasion of Professor John K. Beem's retirement. The articles address problems in differential geometry in general and in particular, global Lorentzian geometry, Finsler geometry, causal boundaries, Penrose's cosmic censorship hypothesis, the geometry of differential operators with variable coefficients on manifolds, and asymptotically de Sitter spacetimes satisfying Einstein's equations with positive cosmological constant. The book is suitable for graduate students and research mathematicians interested in differential geometry.

Differential Geometry and Mathematical Physics

Author : John K. Beem
Publisher : American Mathematical Soc.
ISBN 13 : 0821851721
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Geometry and Mathematical Physics by : John K. Beem

Download or read book Differential Geometry and Mathematical Physics written by John K. Beem and published by American Mathematical Soc.. This book was released on 1994 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.

Differential Geometry Of Warped Product Manifolds And Submanifolds

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

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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.

Geometry, Symmetries, and Classical Physics

Author : Manousos Markoutsakis
Publisher : CRC Press
ISBN 13 : 1000530248
Total Pages : 482 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Geometry, Symmetries, and Classical Physics by : Manousos Markoutsakis

Download or read book Geometry, Symmetries, and Classical Physics written by Manousos Markoutsakis and published by CRC Press. This book was released on 2021-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

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

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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.

Geometry of Submanifolds and Applications

Author : Bang-Yen Chen
Publisher : Springer Nature
ISBN 13 : 981999750X
Total Pages : 230 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Geometry of Submanifolds and Applications by : Bang-Yen Chen

Download or read book Geometry of Submanifolds and Applications written by Bang-Yen Chen and published by Springer Nature. This book was released on with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spaces of Constant Curvature

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
ISBN 13 : 0821852825
Total Pages : 442 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spaces of Constant Curvature by : Joseph Albert Wolf

Download or read book Spaces of Constant Curvature written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 2011 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.

Riemannian Symmetric Spaces of Rank One

Author : Isaac Chavel
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Riemannian Symmetric Spaces of Rank One by : Isaac Chavel

Download or read book Riemannian Symmetric Spaces of Rank One written by Isaac Chavel and published by . This book was released on 1972 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds

Author : Peter B. Gilkey
Publisher : World Scientific
ISBN 13 : 1860947859
Total Pages : 389 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds by : Peter B. Gilkey

Download or read book The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds written by Peter B. Gilkey and published by World Scientific. This book was released on 2007 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory."--BOOK JACKET.

Riemannian Manifolds of Conullity Two

Author : Eric Boeckx
Publisher : World Scientific
ISBN 13 : 981022768X
Total Pages : 319 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Riemannian Manifolds of Conullity Two by : Eric Boeckx

Download or read book Riemannian Manifolds of Conullity Two written by Eric Boeckx and published by World Scientific. This book was released on 1996 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are ?semi-symmetric spaces foliated by Euclidean leaves of codimension two? in the sense of Z I Szab¢. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of ?relative conullity two?. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or ?almost rigid?. The unifying method is solving explicitly particular systems of nonlinear PDE.