Milnor-type theorems for left-invariant Riemannian metrics on Lie groups

摘要

For all left-invariant Riemannian metrics on three-dimensional unimodular Liegroups, there exist particular left-invariant orthonormal frames, so-calledMilnor frames. In this paper, for any left-invariant Riemannian metrics on anyLie groups, we give a procedure to obtain an analogous of Milnor frames, in thesense that the bracket relations among them can be written with relativelysmaller number of parameters. Our procedure is based on the moduli space ofleft-invariant Riemannian metrics. Some explicit examples of such frames andapplications will also be given.