Journal of East China Normal University(Natural Sc

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Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

LIU Jian-cheng, WANG Feng   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2015-12-22 Online:2016-11-25 Published:2017-01-13

Abstract:

In this article we study the maximal space-like submanifold Mn which is isometrically immersed into locally symmetric pseudo-Riemannian manifold Nn+p
p . One main theroem is a sufficient condition for compact Mn to be totally geodesic ones. We also prove a pinching theorem for the square length of the second fundamental form when Mn is complete.

Key words: locally symmetric, maximal, space-like, totally geodesic