Statistical manifolds and their submanifolds. Results on Chen-like invariants
Ion Mihai · Contemporary mathematics - American Mathematical Society · 2020
Statistical manifolds were introduced by S. Amari [Springer, 1985]. They generalize the Hessian manifolds. The geometry of statistical manifolds and their submanifolds is an actual topic of research in pure and applied mathematics. M.E. Aydin, A. Mihai and the present author [Filomat, 2015] obtained geometric inequalities for the scalar curvature and Ricci curvature associated to the dual connections for submanifolds in statistical manifolds of constant curvature. The same authors [Bull. Math. Sci., 2017] proved a generalized Wintgen inequality for such submanifolds. Recently, in co-operation with A. Mihai [Mathematics, 2018], we initiated the study of the geometry of submanifolds in Hessian manifolds of constant Hessian curvature and established a Euler inequality and a Chen-Ricci inequality for such submanifolds. We continue the study of Chen-like invariants on submanifolds in Hessian manifolds of constant Hessian curvature.