Some inequalities on submanifolds in statistical manifolds of constant curvature

Abstract

In this paper, we study the behaviour of submanifolds in statistical manifolds of constant curvature. We investigate curvature properties of such submanifolds. Some inequalities for submanifolds with any codimension and hypersurfaces of statistical manifolds of constant curvature are also established.

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

“…In [3], Aydin and the present authors obtained geometrical inequalities for the scalar curvature and the Ricci curvature associated to the dual connections for submanifolds in statistical manifolds of constant curvature. We want to point-out that, generally, the dual connections are not metric; then one cannot define a sectional curvature with respect to them by the standard definitions.…”

“…Geometric inequalities for statistical submanifolds in statistical manifolds with constant curvature were obtained in [3].…”

Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature

“…Geometric inequalities for statistical submanifolds in statistical manifolds with constant curvature were obtained in [2].…”

Optimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed with Semi-Symmetric Non-Metric Connections

“…So the study of this topic has attracted a lot of attention in the last two decades. Many Chen invariants and inequalities exist for the different classes of submanifolds in various ambient spaces; see [2][3][4][5][6][7][8] and reference therein.…”