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

共 50 条

[1] SHORT GEODESIC SEGMENTS BETWEEN TWO POINTS ON A CLOSED RIEMANNIAN MANIFOLD
Nabutovsky, Alexander
Rotman, Regina
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2009, 19 (02) : 498 - 519
[2] On Conjugate Points and Geodesic Loops in a Complete Riemannian Manifold
Shicheng Xu
The Journal of Geometric Analysis, 2016, 26 : 2221 - 2230
[3] On Conjugate Points and Geodesic Loops in a Complete Riemannian Manifold
Xu, Shicheng
JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (03) : 2221 - 2230
[4] The length of a shortest geodesic net on a closed Riemannian manifold
Rotman, Regina
TOPOLOGY, 2007, 46 (04) : 343 - 356
[5] Lengths of geodesics between two points on a Riemannian manifold
Nabutovsky, Alexander
Rotman, Regina
ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 13 : 13 - 20
[6] Wide short geodesic loops on closed Riemannian manifolds
Rotman, Regina
JOURNAL OF TOPOLOGY AND ANALYSIS, 2024,
[7] GEODESIC FLOWS ON CLOSED RIEMANNIAN MANIFOLDS WITHOUT FOCAL POINTS
PESIN, JB
MATHEMATICS OF THE USSR-IZVESTIYA, 1977, 11 (06): : 1195 - 1228
[8] THE LENGTH OF THE SHORTEST CLOSED GEODESIC IN A CLOSED RIEMANNIAN 3-MANIFOLD WITH NONNEGATIVE RICCI CURVATURE
Barbosa, Ezequiel
Wei, Yong
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (09) : 4001 - 4007
[9] EQUATIONS FOR THE ENTROPY OF A GEODESIC FLOW ON A COMPACT RIEMANNIAN MANIFOLD WITHOUT CONJUGATE POINTS
PESIN, YB
MATHEMATICAL NOTES, 1978, 24 (3-4) : 796 - 805
[10] THE VOLUME OF GEODESIC DISKS IN A RIEMANNIAN MANIFOLD
KOWALSKI, O
VANHECKE, L
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1985, 35 (01) : 66 - 77

← 1 2 3 4 5 →