Homogeneous geodesics and the critical points of the restricted Finsler function - P. Habibi; D. Latifi; M. Toomanian (Հայաստանի ԳԱԱ)
In this paper we 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.
Keywords: Mathematics; Science