Spectral characterization and Schrödinger operator of space-like submanifolds

Shichang Shu; Tianmin Zhu

doi:10.1515/auom-2015-0040

Abstract

In this paper, we would like to study space-like submanifolds in a de Sitter spaces S_p^n+p(1). We define and discuss three Schrödinger operators L_H, L_R, L_R/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators L_H, L_R and L_R/H respectively.

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Spectral characterization and Schrödinger operator of space-like submanifolds

Abstract

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