2015 Volume 21 Issue 2 Pages 87-96
We prove that a semi-parallel totally real statistical submanifold with some natural conditions is totally geodesic if it is of non zero constant curvature, which is corresponding to the Kassabov theorem in the submanifold theory of Kähler manifolds. Moreover, we construct four dimensional holomorphic statistical manifolds using g-natural metrics (cf. [1]).