Torus actions on manifolds of positive sectional curvature
Torus actions on manifolds of positive sectional curvature
复制标题
DOI：
10.1007/bf02392966
复制
发表时间：
2003-09
期刊：
影响因子：
3.7
通讯作者：
Burkhard Wilking
中科院分区：
文献类型：
--
作者：
Burkhard Wilking
给出了正曲线流形上等距环面作用的几个新结果。对称秩是由Grove和Searle作为度量黎曼流形(M，9)对称量的一种可能方法而引入的。它被定义为等距群的秩symrank((M，g))=RANK(Iso(M，g))，或者等价于使得d维环在M.Grove和Searle[13]上有效地等距作用的最大数d。Grove和Searle在[13]中证明了，如果M是正截曲率的紧致流形，那么symrank((M，g))~<；[89。他们还研究了等价性的情形，证明了只有当基础流形微分同胚于Cpn，S~，或透镜空间时，才可能发生等价性。
We present several new results on isometric torus actions on positively curved manifolds. The symmetry rank was introduced by Grove and Searle as one possible way to measure the amount of symmetry of a Riemannian manifold (M, 9). It is defined as the rank of the isometry group, symrank ((M, g))= rank (Iso (M, g)), or equivMently as the largest number d such that a d-dimensional torus acts effectively and isometrically on M.Grove and Searle [13] showed that symrank ((M, g))~<[89 provided that M is a compact manifold of positive sectional curvature. They also studied the case of equality and showed that this can only occur if the underlying manifold is diffeomorphic to CP n, S~, or to a lens space.