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ISRN Geometry
Volume 2012 (2012), Article ID 983403, 26 pages
http://dx.doi.org/10.5402/2012/983403
Review Article

A Review on Metric Symmetries Used in Geometry and Physics

University of Windsor, Windsor, ON, Canada N9B 3P4

Received 8 November 2011; Accepted 19 December 2011

Academic Editor: C. Qu

Copyright © 2012 K. L. Duggal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This is a review paper of the essential research on metric (Killing, homothetic, and conformal) symmetries of Riemannian, semi-Riemannian, and lightlike manifolds. We focus on the main characterization theorems and exhibit the state of art as it now stands. A sketch of the proofs of the most important results is presented together with sufficient references for related results.