March 3, 2026

Affine connections on three-dimensional homogeneous spaces

Key Points

The study describes all local three-dimensional homogeneous spaces with their affine connections, highlighting their structures.
Key evidence includes comprehensive descriptions of curvature and torsion tensors in these spaces, enhancing understanding of their geometry.
This analysis uses the algebraic approach alongside methods from the theory of Lie groups and algebras, providing a solid framework.
This work supports further exploration of affine connections, which may lead to deeper insights into geometric properties of spaces.

Abstract

We describe all local three-dimensional homogeneous spaces, allowing affine connections, it is equivalent to the description of effective pairs of Lie algebras, and all invariant affine connections on the spaces together with their curvature, torsion tensors and holonomy algebras. We use the algebraic approach for description of connections, methods of the theory of Lie groups, Lie algebras and homogeneous spaces.

Affine connections on three-dimensional homogeneous spaces

Key Points

Abstract

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