The volume and lengths on a three sphere
微分几何
2007-05-23 v2
摘要
We show that the volume of any Riemannian metric on a three sphere is bounded below by the length of the shortest closed curve that links its antipodal image. In particular, the volume is bounded below by the minimum of the length of the shortest closed geodesic and the minimal distance between antipodal points.
引用
@article{arxiv.math/0003102,
title = {The volume and lengths on a three sphere},
author = {Christopher B. Croke},
journal= {arXiv preprint arXiv:math/0003102},
year = {2007}
}
备注
The revision improves the main result and simplifies the proof