Positively curved cohomogeneity one manifolds and 3-Sasakian geometry
Positively curved cohomogeneity one manifolds and 3-Sasakian geometry
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DOI：
10.4310/jdg/1197320603
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发表时间：
2005-11
影响因子：
2.5
通讯作者：
K. Grove;Burkhard Wilking;W. Ziller
中科院分区：
文献类型：
--
作者：
K. Grove;Burkhard Wilking;W. Ziller
我们给出了所有可能支持正截面曲率不变度量的单连通奇维上齐一流形的详尽描述。在已知的具有正曲率的奇维流形的例子中，除了球面之外，还有两个无穷族的7维Berger空间和13维Bazaikin空间以及一个孤立的7维Berger空间具有这一性质。除了这些例子，事实证明，只有一个孤立的7-流形，和两个无限的7维家庭，潜在地承认不变的共齐性1度量的正曲率。
We give an exhaustive description of all simply connected odd dimensional cohomogeneity one manifolds that can possibly support an invariant metric with positive sectional curvature. Among the known examples of odd dimensional manifolds with positive curvature, apart from spheres, there are two infinite families among the 7-dimensional Eschenburg spaces and 13-dimensional Bazaikin spaces and one isolated 7-dimensional Berger space with this property. In addition to these examples, it turns out that only one isolated 7-manifold, and two infinite 7-dimensional families, potentially admit invariant cohomogeneity one metrics of positive curvature.