First eigenvalue of Schrodinger operator of space-like hypersurfaces

Abstract

We introduce two Schrodinger operators of compact space-like hypersurfaces in a de Sitter space. If the hypersurfaces have constant mean curvature or constant scalar curvature, we obtain some spectral characterisations of totally umbilical space-like hypersurfaces by the first eigenvalue of the Schrodinger operators. References

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