When a homogeneous space admits an invariant affine connection? If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariantconnections. If a homogeneousspace is reductive, then the space admits an invariant connection.Thepurposeoftheworkisadescriptionofthree-dimensionalnon-reductivehomogeneousspaces, admitting invariant affine connections of nonzero curvature only, and the affine connections, curvature and torsion tensors.
