Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces. I

Abstract

The aim of this paper is to describe all invariant affine connections on pseudo-Riemannian homogeneous spaces of dimensions 2 and 3. We present a complete local classification of Riemannian homogeneous spaces which is equivalent to the description of effective pairs of Lie algebras supplied with an invariant nondegenerate symmetric bilinear form on the isotropy module.