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The affine approach to homogeneous geodesics in homogeneous Finsler spaces. (English) Zbl 1424.53076
Summary: In the recent paper [Z. Yan, Monatsh. Math. 182, No. 1, 165–171 (2017; Zbl 1366.53029)], 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.

53C22 Geodesics in global differential geometry
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C30 Differential geometry of homogeneous manifolds
Full Text: DOI arXiv
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