Nonlinear Connections and Description of Photon-like Objects

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures as generators of measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description of such objects in these terms is given.