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LIU Jian-cheng, WANG Feng. Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 119-126. doi: 10.3969/j.issn.1000-5641.2016.06.013
Citation:
LIU Jian-cheng, WANG Feng. Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 119-126. doi: 10.3969/j.issn.1000-5641.2016.06.013
LIU Jian-cheng, WANG Feng. Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 119-126. doi: 10.3969/j.issn.1000-5641.2016.06.013
Citation:
LIU Jian-cheng, WANG Feng. Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 119-126. doi: 10.3969/j.issn.1000-5641.2016.06.013
In this article we study the maximal space-like submanifoldMn which is isometrically immersed into locally symmetric pseudo-Riemannian manifold Nn+p
p . One main theroem is a sufficient condition for compactMn to be totally geodesic ones. We also prove a pinching theorem for the square length of the second fundamental form whenMn is complete.
[ 1 ] CALABI E. Examples of Bernstein problems for some nonlinear equations[J]. Proc Symp Pure Appl Math, 1970,15: 223-230.
[ 2 ] CHENG S Y, YAU S T. Maximal space-like hypersurfaces in the Lorentz Minkowski spaces[J]. Ann of Math,1976, 104: 407-419.
[ 3 ] ISHIHARA T. Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature[J]. Michigan Math J, 1988, 35: 345-352.
[ 4 ] SUN H F. On maximal spacelike submanifolds[J]. J of Geom, 1999, 65: 193-199.
[ 5 ] CHENG Q M, ISHIKAWA S. Complete maximal spacelike submanifolds[J]. Kodai Math J, 1997, 20: 208-217.
[ 6 ] NISHIKAWA S. On maximal spacelike hypersurfaces in a Lorentzian manifold[J]. Nagoya Math J, 1984, 95: 117-124.
[ 7 ] 张志兵, 陈抚良. 局部对称黎曼流形中的极小子流形[J].纯粹数学与应用数学, 2013, 29: 373-381.
[ 8 ] WALI A N, AKANGA J R. Some results on totally real maximal spacelike submanifolds of an indefinite complex space form[J]. Int J Math Anal, 2011, 5: 207-213.
[ 9 ] 吕艳, 廖蔡生. 局部对称空间中极小子流形的一点补充[J].华东师范大学学报(自然科学版), 2003(4): 5-11.
[10] LIU J C, SUN Z Y. On spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces[J]. J Math Anal Appl, 2010, 364: 195-203.
[11] GOLDBERG S I. Curvature and Homology[M]. London: Academic Press, 1962: 92-94.
[12] OMORI H. Isometric immersions of Riemannian manifolds[J]. J Math Soc Japan, 1967, 19: 205-214.
[13] AIYAMA R. The generalized Gauss map of a space-like submanifold with parallel mean curvature vector in a pseudo-Euclidean space[J]. Japan J Math, 1994, 20: 93-114.
[14] AIYAMA R. Compact space-like m-submanifolds in a pseudo-Riemannian sphere Sm+p p (c)[J]. Tokyo J Math, 1995, 18: 81-90.
[15] XU S L, HU Z S. Compact maximal space-like submanifolds in a pseudo-Riemannian spacetime Sm+p p [J]. Northeast Math J, 2006, 22: 253-259.
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