Orthogonality of Homogeneous geodesics on the tangent bundle

Document Type: Research Articles


1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz-IRAN

2 Department of Mathematics, Islamic Azad University, Tabriz Branch, (IAUT), Tabriz, IRAN


Let  $\xi=(G\times_{K} \mathcal{G} / \mathcal{K}, \rho_{\xi}, G/K,\mathcal{G} / \mathcal{K})$  be the associated bundle and $\tau_{G/K}=(T_{G/K},\pi_{G/K},G/K, \textrm{R}^{m})$ be the tangent bundle of special examples of odd dimension solvable Lie groups equipped with left invariant Riemannian metric. In this paper we  prove some  conditions about the existence of homogeneous geodesic  on the base space of $\tau_{G/K}$ and homogeneous (geodesic) vectors on the fiber space of $\xi$.