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Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension

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Abstract

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.

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Acknowledgments

The author would like to thank Professor Shaoqiang Deng for his professional guidance and constant encouragement.

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, 315211, Ningbo, Zhejiang, People’s Republic of China

    Zaili Yan

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  1. Zaili Yan
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Correspondence to Zaili Yan.

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Communicated by A. Constantin.

This research is supported by NSFC (no. 11401425) and K.C. Wong Magna Fund in Ningbo University.

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Yan, Z. Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension. Monatsh Math 182, 165–171 (2017). https://doi.org/10.1007/s00605-016-0933-x

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  • DOI: https://doi.org/10.1007/s00605-016-0933-x

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