Generalized de Rham – Hodge complexes, the related characteristic Chern classes and some applications to integrable multidimensional differential systems on Riemannian manifolds - Bogolubov, N.N.; Prykarpatsky, A.K. (Український математичний журнал, 2007)
The differential-geometric aspects of generalized de Rham – Hodge complexes naturally related with integrable multidimensional 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 multidimensional 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.