Orthogonality of Homogeneous geodesics on the tangent bundle

Details Orthogonality of Homogeneous geodesics on the tangent bundle Orthogonality of Homogeneous geodesics on the tangent bundle

2011-01-10

arxiv.org/abs/1101.1928v1

Mathematics

Differential Geometry

10 pages

Scientific paper

Let $\xi=(G\times_{K} \mathcal{G} / \mathcal{K}, \rho_{\xi}, \emph{G} / \emph{K},\mathcal{G} / \mathcal{K})$ 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 $\xi$ .

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