Three-dimensional homogeneous spaces with invariant affine connections

Abstract

In the work we describe all local three-dimensional homogeneous spaces, allowing affine connections, it is equivalent to the description of effective pairs of Lie algebras, and all invariant affine connections on the spaces together with their curvature, torsion ten-sors and holonomy algebras. We use the algebraic approach for description of connections, methods of the theory of Lie groups, Lie algebras and homoge-neous spaces.