Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension

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• 作者：Zaili Yan
• 关键词：Homogeneous Finsler spaces ; Homogeneous geodesics ; Geodesic vectors
• 刊名：Monatshefte für Mathematik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：182
• 期：1
• 页码：165-171
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：182

文摘

A connected Finsler space (M, F) is said to be homogeneous if it admits a transitive connected Lie group G of isometries. A geodesic in a homogeneous Finsler space (G / H, F) is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of G. In this paper, we study the problem of the existence of homogeneous geodesics on a homogeneous Finsler space, and prove that any homogeneous Finsler space of odd dimension admits at least one homogeneous geodesic through each point.