THE CHARACTERISTIC CHERN-TYPE CLASSES AND INTEGRABILITY OF MULTIDIMENSIONAL DIFFERENTIAL SYSTEMS ON RIEMANNIAN MANIFOLDS

The differential-geometric properties of generalized de Rham-Hodge complexes naturally related with integrable multidimensional differential systems of M. Gromov type are analyzed. The geometric structure of Chern type characteristic classes are studied, special differential invariants of the Chern type are constructed. The integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)