Document Zbl 1332.53067

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Chebarikov, M. S.

On the Ricci curvature of three-dimensional metric Lie algebras. (Russian. English summary) Zbl 1332.53067

Vladikavkaz. Mat. Zh. 16, No. 1, 57-67 (2014).

Summary: In this paper, we get a classification of possible values of the Ricci curvature signature of left invariant Riemannian metrics on three-dimensional Lie groups, that is a specification of some results of J. W. Milnor [Adv. Math. 21, 293–329 (1976; Zbl 0341.53030)]. As an auxiliary problem, we classify three-dimensional nonunimodular metric Lie algebras.

Cited in 2 Documents

MSC:

53C30

Differential geometry of homogeneous manifolds

Keywords:

homogeneous Riemannian manifold; Lie group; metric Lie algebra; three-dimensional Lie group; Ricci operator; eigenvalues of the Ricci operator; Ricci curvature

Citations:

Zbl 0341.53030

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