The article is devoted to differential-geometric constructions in classical and non-commutative statistics, developed in recent years in the works of the Soviet, Japanese and Danish groups of researchers .. The article studies invariant metrics and invariant characteristics of information proximity, evaluated from the bottom generated by them on sets of states uniform topologies. Describes all invariant Riemannian metrics on a variety of sector states. On the sets of classical probability distributions are integrated geodetic equations for the entire family of invariant linear relationships, Delta gammaDelta, gammainmathbb R. The projective structure of all geodetic lines and completely geodetic submanifolds is described; its local latticeness is established; the coincidence is shown, with an accuracy of the multiplier gamma(gamma-1), the RiemannChristoffel curvature tensor.