Statistical immersions between statistical manifolds of constant curvature

Abstract

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.

10 pages