First eigenvalue of Schrodinger operator of space-like hypersurfaces

Abstract

We introduce two Schrödinger 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 Schrödinger operators.