About invariant tensor fields on low dimensional Lie groups

D. S. Voronov^a, O. P. Gladunova^b, E. D. Rodionov^a, V. V. Slavskii<sup>a

a</sup> Altai State Pedagogical Academy, Barnaul, Russia
^b Altai State University, Barnaul, Russia

Abstract: Complete 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.

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

UDC: 514.765

Received: 26.10.2010