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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 595-604
http://dx.doi.org/10.1155/S0161171291000807

Hypersurfaces in a conformally flat space with curvature collineation

1Department of Mathematics and Statistics, University of Windsor, Ontario, Windsor N9B 3P4, USA
2Department of Mathematics, University of New Haven, West Haven 06516, Connecticut, USA

Received 7 February 1990; Revised 13 August 1990

Copyright © 1991 Hindawi Publishing Corporation. 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

We classify the shape operators of Einstein and pseudo Einstein hypersurfaces in a conformally flat space with a symmetry called curvature collineation. We solve the fundamental problem of finding all possible forms of non-diagonalizable shape operators. A physical example of space-time with matter is presented to show that the energy condition has direct relation with the diagonalizability of shape operator.