Torsion free affine connections on three-dimensional homogeneous spaces

Abstract

The purpose of the work is the classification of threedimensional homogeneous spaces with torsion-free invariant affine connections only. In the case considered in the work, a t-equivalence class contains only one space, i.e., invariant affine connections with coinciding geodesics do not exist. The local classification of homogeneous spaces is equivalent to the description of effective pairs of Lie algebras. In this work we use the algebraic approach for description of connections, methods of the theory of Lie groups, Lie algebras and homogeneous spaces.