Wintgen inequality for surfaces in Hessian manifolds

The inequality of Wintgen is a sharp geometric inequality involving the Gauss curvature (intrinsic invariant) and the normal curvature and squared mean curvature (extrinsic invariants), respectively, for surfaces in the 4-dimensional Euclidean space. <br> In the present paper, we obtain a Wintgen inequality for statistical surfaces in 4-dimensional Hessian manifolds of constant Hessian curvature.