The <i>δ</i>(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Abstract

We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the investigation of statistical submanifolds in Hessian manifolds of constant Hessian curvature; this paper represents a development in this topic.

Keywords

• statistical manifolds
• hessian manifolds
• hessian sectional curvature
• scalar curvature
• ricci curvature
• chen inequality