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：
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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.
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页码：498 / 519
页数：21
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