STM Journals Peer-reviewed research from Consortium e-Learning Network

Research & Reviews: Discrete Mathematical Structures

Homogeneous geodesics on the solvable homogeneous principal bundles

  1. Dr. Reza Chavosh Khatamy

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 considerthat $ \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 someresults about the existence of homogeneous geodesics and geodesicvectors on the fiber

Keywords

Support