The affine approach to homogeneous geodesics in homogeneous Finsler spaces
The affine approach to homogeneous geodesics in homogeneous Finsler spaces
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DOI：
10.5817/am2018-5-257
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发表时间：
2017-03
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影响因子：
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通讯作者：
Zdenvek Duvsek
中科院分区：
文献类型：
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作者：
Zdenvek Duvsek
在最近的一篇论文中，有人声称任何奇数维的齐次芬斯勒空间都允许通过任何点的齐次测地线。为了证明，使用了处理等距群李代数还原分解的代数方法。然而，证明存在严重缺陷。在本文中，使用作者在早期论文中提出的仿射方法来研究芬斯勒齐次空间中的齐次测地线。证明了上述说法是正确的，并进一步证明了任何齐次Berwald空间或齐次可逆Finsler空间都承认通过任意点的齐次测地线。
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.