Parallel displacements on the surface of a projective space

The paper is devoted to studies of parallel displacements of directions and planes in linear and nonlinear (in narrow sense) connections along lines on a surface of a projective space considered as the point manifold and the manifold of tangential planes. Parallel displacements are described by means of covariant differentials of quasitensors in the case of nonlinear connections and projective-covariant differentials in linear connections. The work concerns to researches in the area of differential geometry. The research is based on an application of the G. F. Laptev's method of defining a connection in a principal fiber bundle and his method of continuations and scopes, which generalizes the moving frame method and the Cartan's method of exterior forms; the research depends on calculation of exterior differential forms.