Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Abstract

We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.

Keywords

• statistical manifolds
• Hessian manifolds
• Hessian sectional curvature
• scalar curvature
• Ricci curvature