ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա =Известия НАН Армении: Математика =Proceedings of the NAS Armenia: Mathematics

Homogeneous geodesics and the critical points of the restricted Finsler function

Habibi, P. and Latifi, D. and Toomanian, M. (2011) Homogeneous geodesics and the critical points of the restricted Finsler function. Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 46 (1). pp. 75-82. ISSN 00002-3043

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    Abstract

    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.

    Item Type: Article
    Uncontrolled Keywords: Invariant Finsler metrics; Homogeneous geodesics; geodesic vectors, Lie groups.
    Subjects: Q Science > QA Mathematics
    Divisions: UNSPECIFIED
    Depositing User: Bibliographic Department
    Date Deposited: 07 Aug 2012 09:59
    Last Modified: 07 Aug 2012 09:59
    URI: http://mathematics.asj-oa.am/id/eprint/27

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