Связности ненулевой кривизны на однородных пространствах с неразрешимой группой преобразований

Abstract

The purpose of the work is the local classification of three-dimensional homogeneous spaces, admits invariant affine connections nonzero curvature only, description of the connections on those spaces together with their curvature and torsion tensors, holonomy algebras. We have concerned the case of the unsolvable Lie group of transformations. The local classification of homogeneous spaces is equivalent to the description of the effective pairs of Lie algebras. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character.