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Complete space-like submanifolds in locally symmetric semi-definite spaces

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Analysis in Theory and Applications

Abstract

The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Heifei, R. R. China

    Xu Senlin & Chen Dongmei

Authors
  1. Xu Senlin
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  2. Chen Dongmei
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Correspondence to Xu Senlin.

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Supported by NSFC(No. 10371047)

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Senlin, X., Dongmei, C. Complete space-like submanifolds in locally symmetric semi-definite spaces. Anal. Theory Appl. 20, 383–390 (2004). https://doi.org/10.1007/BF02835231

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  • DOI: https://doi.org/10.1007/BF02835231

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