Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (3): 357-364.

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Complete Space-like Submanifolds with Constant Scalar Curvature in de Sitter Spaces

  

  1. 1. College of Mathematics and Information Science, Northwest Normal University2. Department of Mathematics, Hexi University
  • Received:2007-02-01 Online:2009-09-30 Published:2023-06-27
  • About author: LIU Jian-cheng(1968- ), male, native of Zhenyuan, Gansu, a professor of Northwest Normal University, Ph.D., engages in differential geometry.
  • Supported by:
     Supported by the NNSF of China(10871138)；

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Abstract: In this paper, we study the complete space-like submanifold Mn with constant scalar curvature R≤c in the de Sitter space Spn+p(c) and obtain a pinching condition for Mn to be totally umbilical ones. The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.

Key words: space-like submanifold, second fundamental form, scalar curvature

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