Symmetries of Spacetimes and Riemannian Manifolds - Krishan L. Duggal, Ramesh Sharma

Symmetries of Spacetimes and Riemannian Manifolds

Buch | Softcover
218 Seiten
2013 | Softcover reprint of the original 1st ed. 1999
Springer-Verlag New York Inc.
978-1-4613-7425-1 (ISBN)
53,49 inkl. MwSt
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.

Dedication. 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.

Reihe/Serie Mathematics and Its Applications ; 487
Mathematics and Its Applications ; 487
Zusatzinfo X, 218 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie
ISBN-10 1-4613-7425-1 / 1461374251
ISBN-13 978-1-4613-7425-1 / 9781461374251
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