A. G. Kremlyov, Yu. G. Nikonorov, “The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The unimodular case”, Mat. Tr., 2008, Volume 11, Number 2,Pages <nobr>115

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The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The unimodular case

A. G. Kremlyov, Yu. G. Nikonorov

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: This paper gives a complete classification of the possible values of the signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional unimodular Lie groups.

Key words: homogeneous Riemannian manifold, Lie algebra and group, left-invariant Riemannian metric, Ricci curvature.

UDC: 514.765

Received: 14.05.2008