期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Note on a Kind of Submanifolds in the Local Symmetry Space
摘要/Abstract
研究了局部对称完备黎曼流形中的具平行中曲率场的紧致子流形,得到这类子流形的第2基本形式模长平方的一个拼挤定理,主要证明了当Mn是 Nn+p的紧可定向的子流形且具有平行中曲率向量时,∫M3/2s2+8/3(1-W)(p-1)n-1s+(1-2δ-λ|H|)nsdv≥0,其中λ表示M的沿中曲率方向的第2基本形式的最小特征值.
A compact submani fold in the local symmetry and complete Riemann mani fold with parallel mean curvature vector field was studied, and a pinching theo rem of the square of the length of the second fundamental form of this kind of submani folds was given. Prove the main result. Let Mn be a compact submanifold immersed in the local symmet ry space Nn+p, with parallel mean curv ature vector, then ∫M{3/2s2+8/3(1-W)(p-1)n-1s+(1-2W-λ|H|)ns}dv≥0,where λdenote the minimal eigenvalue of the second fundamental forms along the mean curv ature vector direction.