Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case

This paper studies the canonical symmetric connection $\nabla$ associated to any Lie group $G$. The salient properties of are stated and proved. symmetries geodesic system a general linear formulated. results then applied in special case where algebra $\g$ $G$, has codimension one abelian nilradical. conditions that determine symmetry such completely integrated. Finally obtained compared with some four-dimensional groups whose algebras have three-dimensional nilradicals, for which calculations were performed by MAPLE.