论文标题
同构性一个与准曲率的歧管
Cohomogeneity one manifolds with quasipositive curvature
论文作者
论文摘要
在本文中，我们对同一性的分类进行了分类，即承认一个不变的度量标准，除了两个$ 7 $维的家族外，还具有准阳性分段曲率。主要结果从分类中几乎逐字化导致Verdiani和Grove，Wilking和Ziller进行的正曲率。在正面弯曲的情况下使用的三个主要工具，我们将其推广到准确弯曲的同一同构性一个流形的是Wilking的链定理，这是Grove和Searle和Searle和RankEmma的正相弯曲的固定点同质歧管的分类。
In this paper we give a classification of cohomogeneity one manifolds admitting an invariant metric with quasipositive sectional curvature except for two $7$-dimensional families. The main result carries over almost verbatim from the classification results in positive curvature carried out by Verdiani and Grove, Wilking and Ziller. Three main tools used in the positively curved case that we generalized to quasipositively curved cohomogeneity one manifolds are Wilking's Chain Theorem, the classification of positively curved fixed point homogeneous manifolds by Grove and Searle and the Rank Lemma.
