Homogeneous geodesics on the solvable homogeneous principal bundles

Authors

  • Dr. Reza Chavosh Khatamy Islamic Azad University Tabriz Branch, (IAUT). Azarbaijan Sharghi (East Azarbaijan). Tabriz

DOI:

https://doi.org/10.37591/rrdms.v3i2.739

Keywords:

Associated bundle, homogeneous manifold, solvable Lie group, homogeneous vector

Abstract

Let $M=G/K$ be a homogeneous differentiable manifold .We consider the
homogeneous bundle $\Im=(G,\pi,G/K,K)$
and the tangent bundle $\tau_{G/K}$ of $M=G/K$. Let $G$ be a connected Lie group and $K$
a closed subgroup of $G$. We take the Lie algebras $\cal{G}$ and
$\cal{K}$ of $G$ and $K$ respectively and define $\xi=(G\times_{K}
\cal{ G} / \cal {K}, \rho_{\xi}, \emph{G} / \emph{K},\cal {G} /
\cal {K})$ to be the bundle associated with $\Im$. We consider
that $ \xi$ is strongly isomorphic to tangent bundle
$\tau_{G/K}=(T_{G/K},\pi_{G/K},G/K, {\textbf{R}}^{m})$ .\\

In this paper we take $G$ be a solvable Lie group and prove some
results about the existence of homogeneous geodesics and geodesic
vectors on the fiber

Author Biography

  • Dr. Reza Chavosh Khatamy, Islamic Azad University Tabriz Branch, (IAUT). Azarbaijan Sharghi (East Azarbaijan). Tabriz
    Departmant of Mathematics,

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Published

2016-09-08

Issue

Vol. 3 No. 2 (2016)

Section

Research Articles

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