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

Adela Mihai; Ion Mihai

doi:10.3390/e22020164

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

Entropy (Basel). 2020 Jan 31;22(2):164. doi: 10.3390/e22020164.

Authors

Adela Mihai¹, Ion Mihai²

Affiliations

¹ Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania.
² Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania.

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: Chen inequality; Hessian manifolds; Hessian sectional curvature; Ricci curvature; scalar curvature; statistical manifolds.