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WANG Ru shan (College of Maths and Computer Science, Anhui Normal University, 241000,Wuhu, Anhui, China)  
In this paper, by using the method in [1], the closed submanifolds with non zero parallel mean curveture vector in unit sphere is studied. We find the closed submonifolds is a small sphere, Clifford torus, H(r) torus or Veronese surface under certain condition of the square of the length of the second foundamental form and the mean curvature, which improved the result in [3]. Also in the case n=2, we give the characterization of a class of surfaces with Gauss curvature K=0, 13(H 2+1), which developed the results in [7].
【Fund】: 安徽师范大学校青年科研基金资助项目
【CateGory Index】: O189.3
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Chinese Journal Full-text Database 3 Hits
1 CHEN XIANPING (Department of Mathematics);Pseudo-umbilical Submanifolds in Spaces of Constant Curvature[J];Journal of East China Normal University(Natural Science);1989-01
2 Hu Zejun; Sun Zhenzu(Dept. of Math., Zhengzhou University, Zhengzhou 450052);Submanifolds with Parallel Mean Curvature in Spaces of Constant Curvature[J];JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION;1996-01
3 Chen Qing(Department of Mathematics);A Pinching Theorem for lower Dimensional Submanifolds of Unit Sphere[J];Journal of University of Science and Technology of China;1993-02
Chinese Journal Full-text Database 10 Hits
1 Wang Rushan, (Department of Mathematics);A Theorem on Surface with Parallel Nondegenerate Minimal Section[J];Journal of Anhui Normal University(Natural Science);1992-04
2 HE Guo-qing(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Pseudoumbilical Submanifolds in a Riemann Manifold of Quasi Constant Curvature[J];Journal of Anhui Normal University(Natural Science);2006-04
3 Song Weidong(Department of Mathmatics, Anhui Normal University, 241000, Wuhu, Anhui, PRC);THE MINIMAL SUBMANIFOLD WITH FLAT NORMAL BUNDLE IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANNIAN MANIFOLD[J];Journal of Anhui Normal University(Natural Science);1998-02
4 WANG Ru shan(Anhui Normal University, Wuhu 241000, China);Surfaces with Parallel Nondegenerate Minimal Section in Space Form.[J];PURE AND APPLIED MATHEMATICS;2000-01
5 DING Shunhan(Department of Mathmatics, Lishui Teachers University, Lishui 323000,China);Submanifolds with Parallel Mean Curvature on a Unit Sphere[J];Journal of Fujian Normal University(Natural Science);2003-03
6 ZHAO Zheng xin (Tongling Financial and Economic College,Anhui Tongling,244000);Closed Hypersurface with Non-zero Constant Mean Carvature in Unit Sphere S~(n+1)(1)[J];Journal of Huaibei Industry Teachers College (Natural Sciences Edition);2001-02
7 CAI Kai-ren, XU Hui-qun (Faculty of Science, Hangzhou Teachers College, Hangzhou 310036);Instability and Isolation for Yang-Mills Fields over Compact Submanifold of Sphere[J];Chinese Journal of Engineering Mathematics;2005-05
8 SUN Hongan 1 ZHONG Ding xin WU Qingqiong 2 (1.Southern institute of metallurgy; 2.Gannan Teachers' College,Ganzhou 341000,China);Pseudo-Umbilical Submanifolds in a Sphere[J];JOURNAL OF GANNAN TEACHER'S COLLEGE;2000-03
9 WU Qing qiong 1,Deng Wei 2 (1.Dept.of Math.and Comp.Gannan Teacher's College; 2.Dept.of Physics Gannan Teacher's College,Ganzhou 341000,China);The Submanifolds with Parallel Mean Curvature Vector in A Locally Symmetric Riemannian Manifold[J];Journal of Gannan Teacher's College;2002-03
10 DU Li(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China);Submanifolds with Parallel Normalized Mean Curvature Vector in a Unit Sphere[J];Journal of Gansu Sciences;2007-04
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