Differential-geometric aspects of the Gromov differential relationships theory
Abstract:
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.