Milnor-type theorems for left-invariant Riemannian metrics on Lie groups. (English) Zbl 1353.53058

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 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.


53C30 Differential geometry of homogeneous manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)


Zbl 0341.53030
Full Text: DOI arXiv Euclid


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