Anatoliy Prykarpatsky (Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine and AGH University of Science and Technology, Krakow, Poland)

Differential-geometric aspects of the Gromov differential relationships theory

The differential-geometric aspects of generalized de Rham-Hodge complexes naturally related with integrable multi-dimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic classes are studied. Special differential invariants of the Chern type are constructed, their importance for the integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson type nonlinear integrable differential system is considered, its Cartan type connection mapping and related Chern type differential invariants are analized.