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Let  $xi=(Gtimes_{K} mathcal{G} / mathcal{K}, rho_{xi}, G/K,mathcal{G} / mathcal{K})$  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 $xi$.

کلیدواژه ها:

Hadamard matrices ، Tangent bundle ، Homogeneous manifold ، Solvable Lie group ، Homogeneous geodesic