Compact space-like submanifolds with parallel mean curvature vector of a pseudo-Riemannian space. (English) Zbl 0979.53024

Summary: B. Y. Chen [Indiana Univ. Math. J. 20, 1175-1185 (1971; Zbl 0219.53047)] and H. Sun [Tsukuba J. Math. 20, 45-50 (1996; Zbl 0888.53039)] have studied pseudo-umbilical submanifolds. In this paper, we generalize the compact pseudo-umbilical space-like submanifolds with parallel mean curvature in a pseudo-Riemannian space.


53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
Full Text: EuDML


[1] Aiyama R.: Compact Space-like m-submanifolds in a Pseudo-Riemannian Sphere 5\(^{TM}\)+p(c). Tokyo J. Math. 18, 1 (1995), 81-90. · Zbl 0842.53038
[2] Chen B. Y.: Some Results of Chern do Carmo-Kobayashi type and the Length of Second Fundamental Form. Indiana University Math. J. 20 (1971), 1175-1185. · Zbl 0219.53047
[3] Cheng Q. M., Choi S. M.: Complete Space-like Submanifolds with Parallel Mean Curvature Vector of an Indefinite Space Form. Tsukuba J. Math 17, 2 (1993), 497-512. · Zbl 0804.53089
[4] Haizong L.: Complete Space-like Submanifolds in de Sitter Space with Parallel Mean Curvature Vector Satisfying H’2 = 4^-^-. Annals of Global Analusis and Geometry 15 1997, 335-345.
[5] Huafei S.: Pseudo-Umbilical Submanifolds of A Space Form Nn+*\?c). Tsukuba J. Math. 20, 1 (1996), 45-50. · Zbl 0888.53039
[6] Ishihara T.: Maximal Space-like Submanifolds of a Pseudo-Rieamannian Space of constant Curvature. Michigan Math. J. 35 1988, 345-352. · Zbl 0682.53055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.