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.
Highlights
The eigenvectors of the shape operator of a hypersurface of a semi-Pdemannian space need not be all real
Fialkow [1] provided a complete classification of proper Einstein hypersurfaces in an indefinite space form
The aim of this paper is to present an Mgebraic classification of proper/improper Einstein and pseudo Einstein hypersurfaces in a conformMly flat space
Summary
The eigenvectors of the shape operator (second fundamental form operator) of a hypersurface of a semi-Pdemannian space need not be all real. In the latter case the real eigenvectors (principal directions) may not span the tangent space of the hypersurface at every point. Fialkow [1] provided a complete classification of proper Einstein hypersurfaces in an indefinite space form.
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