About invariant tensor fields on low dimensional Lie groups

Voronov D. S. , Gladunova O. P. , Rodionov E. D. , Slavskii V. V.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 2.

Abstract:
About invariant tensor fields on low dimensional Lie groupsComplete classification of possible signatures of the one dimensional curvature operator on three dimensional Lie groups with left-invariant Riemannian metric and complete classification of four-dimensional Lie algebras (up to isomorphism) of Lie groups with left-invariant Riemannian metrics and  harmonic Weyl tensor are given in this paper.

Keywords: Lie algebras, Lie groups, left-invariant Riemannian metrics, one dimensional curvature, harmonic Weyl tensor

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