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OverviewThis 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. Full Product DetailsAuthor: Krishan L. Duggal , Ramesh SharmaPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1999 Volume: 487 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.361kg ISBN: 9781461374251ISBN 10: 1461374251 Pages: 218 Publication Date: 15 November 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand ![]() We will order this item for you from a manufactured on demand supplier. Table of ContentsDedication. Preface. 1. Preliminaries. 2. Semi-Riemannian Manifolds and Hypersurfaces. 3. Lie Derivatives and Symmetry Groups. 4. Spacetimes of General Relativity. 5. Killing and Affine Killing Vector Fields. 6. Homothetic and Conformal Symmetries. 7. Connection and Curvature Symmetries. 8. Symmetry Inheritance. 9. Symmetries of Some Geometric Structures. A: The Petrov Classification. Bibliography. Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |