Analysis in Theory and Applications

, Volume 20, Issue 4, pp 383–390 | Cite as

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

  • Xu Senlin
  • Chen Dongmei


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.

Key words

space-like submanifolds constant mean curvature flat normal bundle second fundamental form locally symmetric semi-definite space 

AMS(2000)subject classification

53C20 53C40 


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Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHeifeiR. R. China

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