Hypersurfaces in a conformally flat space with curvature collineation
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.