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 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.