Invariant affine connections on three-dimensional homogeneous spaces with nonsolvable transformation group

Abstract

© 2014, Pleiades Publishing, Ltd. The aim of this paper is to describe all invariant affine connections on three-dimensional homogeneous spaces with nonsolvable transformation group. We present complete local classification of homogeneous spaces, it is equivalent to the description of effective pairs of Lie algebras. We describe all invariant affine connections together with their curvature and torsion tensors, holonomy algebras.