K. L. Duggal, R. Sharma, "Hypersurfaces in a conformally flat space with curvature collineation", International Journal of Mathematics and Mathematical Sciences, vol. 14, Article ID 714047, 10 pages, 1991. https://doi.org/10.1155/S0161171291000807
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.
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