Milnor-type theorems for left-invariant Riemannian metrics on Lie groups (Q296543)

The authors prove the existence of special left-invariant orthonormal frames for left-invariant Riemannian metrics on Lie groups. This means that the bracket relations among them can be written with a relatively smaller number of parameters. This result could be considered as a generalization of well-known results of \textit{J. W. Milnor} on 3-dimensional unimodular Lie groups [Adv. Math. 21, 293--329 (1976; Zbl 0341.53030)]. The main tool is based on the structure of the moduli space of left-invariant Riemannian metrics. The authors consider some explicit examples of such frames and some applications.