Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

тензор кривизны

Non-reductive spaces with equiaffine connections of nonzero curvature

The introduction of this article states the object of our investigation which is structures on homogeneous spaces. The problem of establishing links between the curvature and the structure of a manifold is one of the important problems of geometry. In general, the research of manifolds of various types is rather complicated. Therefore, it is natural to consider this problem in a narrower class of non-reductive homogeneous spaces. If a homogeneous space is reductive, then the space admits an invariant connection.

Connections of Nonzero Curvature on Three-dimensional Non-reductive Spaces

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.