# The affine approach to homogeneous geodesics in homogeneous Finsler spaces

Archivum Mathematicum (2018)

- Volume: 054, Issue: 5, page 257-263
- ISSN: 0044-8753

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topDušek, Zdeněk. "The affine approach to homogeneous geodesics in homogeneous Finsler spaces." Archivum Mathematicum 054.5 (2018): 257-263. <http://eudml.org/doc/294673>.

@article{Dušek2018,

abstract = {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.},

author = {Dušek, Zdeněk},

journal = {Archivum Mathematicum},

keywords = {homogeneous space; Finsler space; Killing vector field; homogeneous geodesic},

language = {eng},

number = {5},

pages = {257-263},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {The affine approach to homogeneous geodesics in homogeneous Finsler spaces},

url = {http://eudml.org/doc/294673},

volume = {054},

year = {2018},

}

TY - JOUR

AU - Dušek, Zdeněk

TI - The affine approach to homogeneous geodesics in homogeneous Finsler spaces

JO - Archivum Mathematicum

PY - 2018

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 054

IS - 5

SP - 257

EP - 263

AB - 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.

LA - eng

KW - homogeneous space; Finsler space; Killing vector field; homogeneous geodesic

UR - http://eudml.org/doc/294673

ER -

## References

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