Address: Institute of Technology and Business in České Budějovice, Okružní 517/10, 370 01 České Budějovice, Czech Republic
E-mail: zdusek@mail.vstecb.cz
Abstract: The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.
AMSclassification: primary 53C22; secondary 53C60, 53C30.
Keywords: homogeneous space, Finsler space, Randers space, homogeneous geodesic.
DOI: 10.5817/AM2019-5-281