Cyclic Finser metrics on homogeneous spaces

2023/04/03 by Ju Le Tan, Ming Xu, Tan, Ju +1
Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2304.01034

openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we generalize the notion of cyclic metric to homogeneous Finsler geometry. Firstly, we prove that a homogeneous Finsler space (G/H, F) must be symmetric when it satisfies the naturally reductive and cyclic conditions simultaneously. Then we prove that a Finsler cyclic Lie group which is either flat or nilpotent must have an Abelian Lie algebra. Finally, we show how to induce a cyclic (α,β) metric from a cyclic Riemannian metric. Using this method, we construct a Randers cyclic Lie group.

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