  The condition for the curvature of a statistical manifold to admit a kind of
standard hypersurface is given. We study the statistical hypersurfces of some
types of the statistical manifolds $(M, \nabla, g )$, which enable $(M,
\nabla^{(\alpha)}, g ), \forall\alpha\in\mathbf{R}$ to admit the structure of a
constant curvature.
