A sphere theorem for reverse volume pinching on even-dimensional manifolds
A sphere theorem for reverse volume pinching on even-dimensional manifolds
复制标题
偶维流形上反体积箍缩的球体定理
DOI：
10.1090/s0002-9939-1991-1042262-0
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Yoe Itokawa
中科院分区：
文献类型：
--
作者：
Leslie Coghlan;Yoe Itokawa
设M是偶数维d的紧致单连通黎曼流形。众所周知，如果M的截面曲率位于范围（0，A]内，则M的体积大于或等于具有常曲率A的d维欧几里得球面Sd的体积。证明了若M的体积不大于Sd的3/2倍，则M与球面同胚.
Let M be a compact simply connected riemannian manifold of even dimension d . It is well known that if the sectional curvature of M lies in the range (0, A], then M has volume greater than or equal to that of the d-dimensional euclidean sphere Sd of constant curvature A. We prove that d if the volume of M is no greater than 3/2 times that of Sd, then M is homeomorphic with the sphere.