International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1991 / Article

Open Access

Volume 14 |Article ID 714047 | 10 pages | https://doi.org/10.1155/S0161171291000807

Hypersurfaces in a conformally flat space with curvature collineation

Received07 Feb 1990
Revised13 Aug 1990

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.

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.


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