Konovenko N. Structures of differential invariants algebras for classical -geometries

The dissertation is devoted to local investigation of geometries on one and two-dimensional manifolds equipped with sl_2 -action. It is shown that the differential invariants algebra posesses a poisson structure. This structure is used for the description of differential invariants algebras for the case of Lobachevsky’s and de Sitter’s geometry. Results of the dissertation can be used in differential geometry for classification of various geometrical quantities such as tensors, differential forms, differential operators, and in applications to mathematical physics and differential equations.