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Symmetries of Spacetimes and Riemannian Manifolds

  • Krishan L. Duggal
  • Ramesh Sharma

Part of the Mathematics and Its Applications book series (MAIA, volume 487)

Table of contents

  1. Front Matter
    Pages i-x
  2. Krishan L. Duggal, Ramesh Sharma
    Pages 1-9
  3. Krishan L. Duggal, Ramesh Sharma
    Pages 10-35
  4. Krishan L. Duggal, Ramesh Sharma
    Pages 36-55
  5. Krishan L. Duggal, Ramesh Sharma
    Pages 56-78
  6. Krishan L. Duggal, Ramesh Sharma
    Pages 79-102
  7. Krishan L. Duggal, Ramesh Sharma
    Pages 103-133
  8. Krishan L. Duggal, Ramesh Sharma
    Pages 134-155
  9. Krishan L. Duggal, Ramesh Sharma
    Pages 156-172
  10. Krishan L. Duggal, Ramesh Sharma
    Pages 173-192
  11. Back Matter
    Pages 193-217

About this book

Introduction

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.

Keywords

Lie group curvature differential geometry geometry manifold relativity theory of relativity

Authors and affiliations

  • Krishan L. Duggal
    • 1
  • Ramesh Sharma
    • 2
  1. 1.University of WindsorCanada
  2. 2.University of New HavenUSA

Bibliographic information