| 何太平,罗宏.常曲率空间中具正Ricci曲率的子流形[J].数学年刊A辑,2011,32(6):679~686 |
| 常曲率空间中具正Ricci曲率的子流形 |
| Submanifolds with Positive Ricci Curvature in the Constant Curvature Space |
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| DOI： |
| 中文关键词: Ricci曲率 伪脐 直积 |
| 英文关键词:Ricci curvature Pseudo-umbilicus Direct product |
| 基金项目:国家自然科学基金(No11071177)资助的项目 |
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| 中文摘要: |
| 设$S^{n+p}(1)$是一单位球面,
$M^{n}$ 是浸入$S^{n+p}(1)$的具有非零平行平均曲率向量的$n$维紧致子流形.
证明了当$n \geq 4$, $p \geq
2$时, 如果$M^{n}$的Ricci曲率不小于$(n-2)(1+H^2)$, 则$M^{n}$
是全脐的或者$M^{n}$的Ricci曲率等于$(n-2)(1+H^2)$, 进而 $M^{n}$的几何分类被完全给出. |
| 英文摘要: |
| Let $S^{n+p}(1)$ be a unit sphere,
$M^{n}$ an $n$-dimensional compact submanifold immersed in $S^{n+p}(1)$ with non-zero parallel mean curvature vector
. It is proved that when $n \geq 4$ and $p \geq
2$, if the Ricci curvature of $M^{n}$ is not less than $(n-2)(1+H^2)$, then $M^{n}$
is totally umbilical, or the Ricci curvature of $M^{n}$ equals to $(n-2)(1+H^2)$, and
so the geometry classification of $M^{n}$ is given. |
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