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

Abstract

Math. 237:87-95, 2008), independently. In the present paper we establish a generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature.

Some Results on Statistical Hypersurfaces of Sasakian Statistical Manifolds and Holomorphic Statistical Manifolds

“…Moreover, many other geometric inequalities in classical Riemannian geometry have been generalized to various statistical manifolds. For instance, M. E. Aydin, A. Mihai and I. Mihai [4] obtained the generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature; B. Y. Chen, A. Mihai, and I. Mihai [7] proved the Chen first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Also, some other results in Riemannian geometry can be generalized to the geometry of statistical manifolds.…”

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

“…The curvature invariants of statistical submanifolds in different ambient spaces were recently studied by several authors, for example in Kenmotsu statistical manifolds of constant -sectional curvature (see [ 10 ]). Also, a generalized Wintgen inequality for statistical submanifolds was obtained in [ 11 ].…”

Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature

“…In particular, the differential geometry field is focused on topics such as submanifold theory of statistical manifolds [33], Hessian geometry [34], statistical submersions [35], complex manifold theory of statistical manifolds ( [29,36,37]), contact theory on statistical manifolds [38], and quaternionic theory on statistical manifolds [39]. For the above problems, Aydin et al obtained Chen-Ricci inequalities [40] and a generalized Wintgen inequality [41] for submanifolds in statistical manifolds of constant curvature. Moreover, Lee et al established optimal inequalities involving the Casorati curvatures and the normalized scalar curvature on submanifolds of statistical manifolds of constant curvature [42].…”