Abstract:
We consider a procedure to obtain Milnor-type theorems ([1]) by constructing a special orthonormal frames
(Milnor's frames) of metric Lie algebras in dimension 4. This method is based on the results [2], devoted to the study of spaces of
left-invariant Riemannian metrics on Lie groups. These frames are useful for computing the invariant tensor fields on Lie groups with left-invariant Riemannian metrics.
References:
[1] J. Milnor, "‘Curvatures of left invariant metrics on Lie groups"’, Adv. Math. 21(3), 293–
329 (1976).
[2] H. Kodama, A. Takahara, H. Tamaru, "‘The space of left-invariant metrics on a Lie group
up to isometry and scaling"’, Manuscripta Math. 135, 229–243 (2011).
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