Symmetries of Spacetimes and Riemannian Manifolds

1. Front Matter

   Pages i-x

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2. Preliminaries

   • Krishan L. Duggal, Ramesh Sharma

   Pages 1-9

3. Semi-Riemannian Manifolds and Hypersurfaces

   • Krishan L. Duggal, Ramesh Sharma

   Pages 10-35

4. Lie Derivatives and Symmetry Groups

   • Krishan L. Duggal, Ramesh Sharma

   Pages 36-55

5. Spacetimes of General Relativity

   • Krishan L. Duggal, Ramesh Sharma

   Pages 56-78

6. Killing and Affine Killing Vector Fields

   • Krishan L. Duggal, Ramesh Sharma

   Pages 79-102

7. Homothetic and Conformal Symmetries

   • Krishan L. Duggal, Ramesh Sharma

   Pages 103-133

8. Connection and Curvature Symmetries

   • Krishan L. Duggal, Ramesh Sharma

   Pages 134-155

9. Symmetry Inheritance

   • Krishan L. Duggal, Ramesh Sharma

   Pages 156-172

10. Symmetries of Some Geometric Structures

    • Krishan L. Duggal, Ramesh Sharma

    Pages 173-192

11. Back Matter

    Pages 193-217

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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.

• Lie group
• curvature
• differential geometry
• geometry
• manifold
• relativity
• theory of relativity
• partial differential equations

• University of Windsor, Canada

  Krishan L. Duggal

• University of New Haven, USA

  Ramesh Sharma

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