测地线
数学
素数(序理论)
轨道(动力学)
等变映射
纯数学
秩(图论)
维数(图论)
同种类的
歧管(流体力学)
公制(单位)
芬斯勒流形
空格(标点符号)
数学分析
组合数学
几何学
计算机科学
曲率
航空航天工程
经济
工程类
操作系统
机械工程
运营管理
标量曲率
标识
DOI:10.1007/s11425-018-9454-y
摘要
When a closed Finsler manifold admits continuous isometric actions, estimating the number of orbits of prime closed geodesics seems a more reasonable substitution for estimating the number of prime closed geodesics. To extend the results of Duan, Long, Rademacher, Wang and others on the existence of two prime closed geodesics to the equivariant situation, we propose the question if a closed Finsler manifold has only one orbit of prime closed geodesics if and only if it is a compact rank-one Riemannian symmetric space. In this paper, we study this problem in homogeneous Finsler geometry, and get a positive answer when the dimension is even or the metric is reversible. We guess the rank inequality and the algebraic techniques in this paper may continue to play an important role for discussing our question in the non-homogeneous situation.
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