Skip to main content
SpringerLink
Log in

Symmetries of Spacetimes and Riemannian Manifolds

  • Book
  • © 1999

Overview

Authors:
  1. Krishan L. Duggal

    1. University of Windsor, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Ramesh Sharma

    1. University of New Haven, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  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
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • University of Windsor, Canada

    Krishan L. Duggal

  • University of New Haven, USA

    Ramesh Sharma

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation