Zdeněk Dušek
Published 2017-03-03Version 1
In a recent paper, it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. For the proof, the algebraic method dealing with the reductive decomposition of the Lie algebra of the isometry group was used. However, the proof contains a serious gap. In the present paper, homogeneous geodesics in Finsler homogeneous spaces are studied using the affine method, which was developed in earlier papers by the author. The mentioned statement is proved correctly and it is further proved that any homogeneous Berwald space or homogeneous reversible Finsler space admits a homogeneous geodesic through any point.
On the Existence of Homogeneous Geodesics in Homogeneous $(α,β)$-Spaces
Homogeneous geodesics in homogeneous Finsler spaces
Homogeneous Finsler space with infinite series $(α, β)$-metric
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