Geodesic
The affine approach to homogeneous geodesics in homogeneous Finsler spaces
Archivum mathematicum, Tome 54 (2018) no. 5, pp. 257-263 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2018-5-257
Classification : 53C22, 53C30, 53C60
Keywords: homogeneous space; Finsler space; Killing vector field; homogeneous geodesic 
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Dušek, Zdeněk. The affine approach to homogeneous geodesics in homogeneous Finsler spaces. Archivum mathematicum, Tome 54 (2018) no. 5, pp. 257-263. doi: 10.5817/AM2018-5-257

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