Short Geodesic Segments between Two Points on a Closed Riemannian Manifold

被引：0

作者：

Alexander Nabutovsky

Regina Rotman

机构：

[1] University of Toronto,Department of Mathematics

[2] Penn State University,Department of Mathematics

来源：

Geometric and Functional Analysis | 2009年 / 19卷

关键词：

Geodesic loops; lengths of geodesics; geometry of loop spaces; length functional; 53C23; 53C22; 58E10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let Mn be a closed Riemannian manifold homotopy equivalent to the product of S2 and an arbitrary (n–2)-dimensional manifold. In this paper we prove that given an arbitrary pair of points on Mn there exist at least k distinct geodesics of length at most 20k!d between these points for every positive integer k. Here d denotes the diameter of Mn.

引用

页码：498 / 519

页数：21

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