Hypersurfaces in a conformally flat space with curvature collineation - K. L. Duggal; R. Sharma (International Journal of Mathematics and Mathematical Sciences)
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.