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Title: The affine approach to homogeneous geodesics in homogeneous Finsler spaces (English)
Author: Dušek, Zdeněk
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 5
Year: 2018
Pages: 257-263
Summary lang: English
Category: math
Summary: In the recent paper [Yan, Z.: Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension, Monatsh. Math. 182,1, 165–171 (2017)], it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. However, the proof contains a serious gap. The situation is a bit delicate, because the statement is correct. In the present paper, the incorrect part in this proof is indicated. Further, it is shown that homogeneous geodesics in homogeneous Finsler spaces can be studied by another method developed in earlier works by the author for homogeneous affine manifolds. This method is adapted for Finsler geometry and the statement is proved correctly. (English)
Keyword: homogeneous space
Keyword: Finsler space
Keyword: Killing vector field
Keyword: homogeneous geodesic
MSC: 53C22
MSC: 53C30
MSC: 53C60
idZBL: Zbl 06997354
idMR: MR3887353
DOI: 10.5817/AM2018-5-257
Date available: 2018-12-06T16:12:43Z
Last updated: 2020-01-05
Stable URL:
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