On Riemannian manifolds with positive weighted Ricci curvature of negative effective dimension
On Riemannian manifolds with positive weighted Ricci curvature of negative effective dimension
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DOI：
10.2206/kyushujm.73.205
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发表时间：
2017-04
期刊：
影响因子：
--
通讯作者：
Cong Hung Mai
中科院分区：
文献类型：
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作者：
Cong Hung Mai
本文研究了当有效维数为负时，满足加权Ricci曲率下界$\mathrm{Ric}_{N} \geq K$且K>0$的完备黎曼流形，作为经典Obata刚性定理的一个对应.我们的主要定理表明，如果$N<-1 $并且达到最小值，则流形作为双曲性质的翘曲积从真实的线分裂。
In this paper, we investigate complete Riemannian manifolds satisfying the lower weighted Ricci curvature bound $\mathrm{Ric}_{N} \geq K$ with $K>0$ for the negative effective dimension $N 0$, as a counterpart to the classical Obata rigidity theorem. Our main theorem shows that, if $N<-1$ and the minimum is attained, then the manifold splits off the real line as a warped product of hyperbolic nature.