Zoll黎曼度量的极小极大刻画
微分几何
2022-05-03 v2 代数拓扑
几何拓扑
摘要
我们将给定单连通自旋闭流形上的Zoll黎曼度量刻画为：其有限维环路空间中两个适当的极小极大值重合的那些黎曼度量。我们还证明，在奇维黎曼球面上，当环路空间中某些极小极大对重合时，每一点都位于一条闭测地线上。
引用
@article{arxiv.1809.08689,
title = {A min-max characterization of Zoll Riemannian metrics},
author = {Marco Mazzucchelli and Stefan Suhr},
journal= {arXiv preprint arXiv:1809.08689},
year = {2022}
}
备注
24 pages, 1 figure; version 2: Theorem 1.1 now stated for manifolds homeomorphic to odd-dimensional spheres (the original statement was correct, but indeed the assumptions made on the manifold forced it to be a topological sphere according to Bott-Samelson theorem and the Poincar\'e conjecture); minor correction in the centered equation before (5.5)