Sharp estimates and the Dirac operator
Sharp estimates and the Dirac operator
复制标题
DOI：
10.1007/s002080050136
复制
发表时间：
1998
影响因子：
1.4
通讯作者：
Marcelo Llarull
中科院分区：
文献类型：
--
作者：
Marcelo Llarull
本文建立并推广了M.其中指出，每一个严格优于标准度量的黎曼度量必须有严格小于的标量曲率。更一般地说，如果是任何维数的紧致自旋流形，它允许一个非零度的距离递减映射，那么要么存在一个具有归一化标量曲率的点，要么等距于。距离递减假设可以用较弱的收缩形式来代替。在这两种情况下，结果都是尖锐的。给出了一个反例，证明了用-形式代替2-形式时，结果不再成立。
This paper establishes and extends a conjecture posed by M. Gromov which states that every riemannian metriconthat strictly dominates the standard metricmust have somewhere scalar curvature strictly less than that of. More generally, ifis any compact spin manifold of dimensionwhich admits a distance decreasing mapof non-zero degree, then either there is a pointwith normalized scalar curvature, oris isometric to. The distance decreasing hypothesis can be replaced by the weaker assumptionis contracting on-forms. In both cases, the results are sharp. An explicit counterexample is given to show that the result is no longer valid if one replaces 2-forms by-forms with.