Non-reductive homogeneous spaces, admitting affine connections

Abstract

The purpose of the work is a study of three-dimensional non-reductive homogeneous spaces, admitting invariant affine connections, description of the affine connections together with their curvature and torsion tensors, holonomy algebras. We describe all three-dimensional non-reductive homogeneous spaces, allowing invariant affine connections (the local classification of such spaces is equivalent to the description of the effective pairs of Lie algebras) and all invariant affine connections on the spaces together with their curvature and torsion tensors, holonomy algebras. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character.