The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ-manifolds are introduced. New conformal invariant tools are defined. A necessary condition for the f-conformal equivalence of γ-manifolds is found, extending that for the α-conformal equivalence for statistical manifolds. Certain examples of these new defined geometrical objects are given in the theory of Iinformation.
