The first eigenvalue of spacelike submanifolds in indefinite space form $R^{n+p}_p$

Yingbo Han and Shuxiang Feng

Address: College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, P. R. China


Abstract: In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in $R^{n+p}_p$ with the bounded Gauss map must be zero.

AMSclassification: primary 53C42; secondary 53B30.

Keywords: spacelike submanifolds, the first eigenvalue.