The minimal number of homogeneous geodesics depending on the signature of the Killing form


  • Zdeněk Dušek Institute of Technology and Business in České Budějovice, Okružní 517/10, 370 01 České Budějovice, Czech Republic



The existence of at least two homogeneous geodesics in any homogeneous Finsler manifold was proved in a previous paper by the author. The examples of solvable Lie groups with invariant Finsler metric which admit just two homogeneous geodesics were presented in another paper. In the present work, it is shown that a homogeneous Finsler manifold with indefinite Killing form admits at least four homogeneous geodesics. Examples of invariant Randers metrics on Lie groups with definite Killing form admitting just two homogeneous geodesics and examples with indefinite Killing form admitting just four homogeneous geodesics are presented.


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