The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank
The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank
复制标题
DOI：
10.1090/s0002-9939-01-06039-7
复制
发表时间：
2001-06
期刊：
影响因子：
--
通讯作者：
Thomas Puettmann;C. Searle
中科院分区：
文献类型：
--
作者：
Thomas Puettmann;C. Searle
本文证明了具有正（非负）截面曲率的偶数维紧致流形的Euler特征是正（非负）的，只要该流形允许紧致李群G的等距作用，该李群G具有主各向同性群H和上齐性k，使得k -（rankG - rank H）l.
We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group G with principal isotropy group H and cohomogeneity k such that k - (rankG - rank H) l.