Parastoo Habibi - Department of Mathematics, Islamic Azad University, Astara branch, Astara, Iran. E-mail: p.habibi@iau-astara.ac.ir

In this paper we consider invariant square metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces. We study geodesic vectors and investigates the set of all homogeneous geodesics on two-step nilpotent Lie groups of dimension five.

square metric, Geodesic vector, two-step nilpotent Lie group