Killing\u27s Equations for Invariant Metrics on Lie Groups

Abstract

This article is the first in a series that will investigate symmetry and curvature properties of a right-invariant metric on a Lie group. This talk will consider Lie groups in dimension two and three and will focus on the solutions of Killing\u27s equations. A striking result is that several of the three-dimensional Lie groups turn out to be spaces of constant curvature