Pseudo-umbilical space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

doi:10.3969/j.issn.1000-5641.2019.03.002

Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (3): 6-12.doi: 10.3969/j.issn.1000-5641.2019.03.002

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Pseudo-umbilical space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

BAI Hui-run, LIU Jian-cheng

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2018-04-04 Online:2019-05-25 Published:2019-05-30

Abstract

Abstract: In this paper, we study the pseudo-umbilical space-like submanifolds Mⁿ which are immersed into locally symmetric pseudo-Riemannian manifolds N_p^n+p. When Mⁿ is complete non-compact and has a parallel mean curvature vector field, a pinching theorem for the square length of the second fundamental form of Mⁿ is obtained. When Mⁿ is compact and has a parallel mean curvature vector field, then we prove that Mⁿ is totally geodesic.

Key words: pseudo-Riemannian manifold, parallel mean curvature field, pseudoumbilical, second fundamental form

CLC Number:

O186.12

BAI Hui-run, LIU Jian-cheng. Pseudo-umbilical space-like submanifolds in locally symmetric pseudo-Riemannian manifolds[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 6-12.

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Pseudo-umbilical space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

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