THREE-DIMENSIONAL SYMMETRIC SPACES, ADMITS UNCANONICAL CONNECTIONS
The purpose of the work is the description of three-dimensional symmetric homogeneous spaces, admits uncanonical connections, invariant affine connections on those spaces. The basic notions, such as an isotropically-faithful pair, an affine connection, curvature and torsion tensors, a symmetric space are defined. The local description of three-dimensional symmetric homogeneous spaces, admitting uncanonical connections, is given. The local classification of such spaces is equivalent to the description of the effective pairs of Lie algebras. All invariant affine connections on those spaces are described. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character. The peculiarity of techniques presented in the work is the application of purely algebraic approach, as well as the compound of methods of differential geometry, the theory of Lie groups and algebras and the theory of homogeneous spaces.