Submanifold Sectional Curvature And Special Equations Of Hesse Manifoldsh

H.Shima and K.Yagi gave the equivalent conditions of Hes-sian measurement and several constant equations of Hessian man-ifold in 1977. Although properties of Hessian manifold were deeply investigated, Gauss equation and Codazzi equation of Hes-sian submanifold were not involved. In the thesis, Gauss equa-tion and Codazzi equation of Hessian submanifold were obtained from corresponding equations of Riemannian manifold.The sec-tional curvature of Hessian manifold was analyzed and demon-strated. An interesting relationship between Hessian sectional curvature and Riemannian curvature was discovered and proved.