Spectral characterization and Schrödinger operator of space-like submanifolds
and | Apr 22, 2017
Published Online: Apr 22, 2017
Page range: 241 - 257
Received: Nov 01, 2012
Accepted: Sep 01, 2014
DOI: https://doi.org/10.1515/auom-2015-0040
Keywords
© 2017
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
In this paper, we would like to study space-like submanifolds in a de Sitter spaces Spn+p(1). We define and discuss three Schrödinger operators LH, LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH, LR and LR/H respectively.