Совершенные алгебры голономии тривиальных связностей на однородных пространствах неразрешимых групп Ли

Abstract

In this article we present a local classification of three-dimensional reductive homogeneous spaces allowing a normal connection. We have concerned the case of the unsolvable Lie group of transformations with a solvable stabilizer. We describe all invariant affine connections together with their curvature and torsion tensors, canonical connections and natural torsion-free connections. We have studied the holonomy algebras of homogeneous spaces and have found when the invariant connection is normal.