Homogeneous geodesics and the critical points of the restricted Finsler function |
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Authors: | Parastoo Habibi Dariush Latifi Megerdich Toomanian |
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Institution: | 1. Astara branch, Islamic Azad University, Shahrekord, Iran 2. University of Mohaghegh Ardabili, Ardebili, Iran 3. Karaj branch, Islamic Azad University, Shahrekord, Iran
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Abstract: | In this paperwe study the set of homogeneous geodesics of a left-invariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. We extend J. Szenthe’s result on homogeneous geodesics to left-invariant Finsler metrics. This result gives a relation between geodesic vectors and restricted Minkowski norm in Finsler setting. We show that if a compact connected and semisimple Lie group has rank greater than 1, then for every left-invariant Finsler metric there are infinitely many homogeneous geodesics through the identity element. |
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