A survey on curvatures of Hessian manifolds

This paper deals with the relationship of curvatures between Hessian and Riemannian manifolds. By making use of the methods of Shima [Shima H. Hessian manifolds of constant Hessian sectional curvature. J Math Soc Jpn 1995;47(4):735–53] we investigate a new approach to the curvatures of a manifold. Finally, some results are mentioned in the concluding remarks.