A Note on Pseudo-Umbilical Submanifolds of Hessian Manifolds with Constant Hessian Sectional Curvature

The geometry of Hessian manifold, as a branch of statistics, physics, Kaehlerian, and affine differential geometry, is deeply fruitful and a new field for scientists. However, inspite of its importance submanifolds and curvature conditions of it have not been so well known yet. In this paper, we focus on the pseudo-umbilical submanifolds on Hessian manifold with constant Hessian sectional curvature and using sectional curvature conditions we obtain new results on it.