General Chen Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Abstract

Chen’s first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature was obtained by B.-Y. Chen et al. Other particular cases of Chen inequalities in a statistical setting were given by different authors. The objective of the present article is to establish the general Chen inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature.

Keywords

• Hessian manifolds
• constant Hessian curvature
• statistical submanifolds
• Chen inequalities