http://www.paper.edu.cn
关于二维对称 Finsler 球面上闭测地线的存在
性的一点注记
段华贵
1
,龙以明
2
1
南开大学数学科学学院,天津 300071
2
南开大学陈省身数学研究所,天津 300071
摘要:在本文中,我们证明了二维对称 Finsler 球面上存在无穷多条几何相异的闭测地线.
关键词:闭测地线,对称 Finsler 度量, 2 维球面, 几何相异.
中图分类号: O186.16
A remark on the existence of closed geodesics on
symmetric Finsler 2-spheres
Huagui Duan
1
, Yiming Long
2
1
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071
2
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071
Abstract: In this paper, we proved the existence of infinitely many geometrically different
closed geodesics for every symmetric Finsler metric on two-spheres.
Key words: closed geodesics, symmetric Finsler metric, two-spheres, geometrically different.
0 Introduction
The study on closed geodesics on spheres is a classical and important problem in both
dynamical systems and differential geometry. Bangert [1] in 1993 and Franks [2] in 1992 proved
that for every Riemannian metric on S
2
there exist infinitely many geometrically distinct closed
geodesics. And Bangert [1] reads: One can ask if there exist infinitely many closed geodesics
for every symmetric Finsler metric on S
2
. And there is a good chance that this is indeed so.
The purpose of this paper is to answer this problem positively, i.e., we obtain the following
Theorem 0.1.
Theorem 0.1. There exist infinitely many geometrically different closed geodesics on
every symmetric Finsler 2-sphere (S
2
, F ).
On the corresponding problems on the symmetric Finsler 2-spheres, we refer readers to
p.155-156 of [3].
基金项目: Partially supported by SRFDP (200800551002) and NNSFC (11131004).
作者简介: Duan Huagui(1977-),male,major research direction:nonlinear analysis, E-mail: duanhg@nankai.edu.cn.
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