P. Wintgen proved in Sur l'inégalité de Chen-Willmore. CR Acad. Sci. Paris 288, 993–995
(1979) that the Gauss curvature G and the normal curvature K^D of a surface in the …

In this paper, we study statistical manifolds and their submanifolds. We first construct two
new examples of statistical warped product manifolds and give a method how to construct …

The Wintgen inequality (1979) is a sharp geometric inequality for surfaces in the 4-
dimensional Euclidean space involving the Gauss curvature (intrinsic invariant) and the …

In this paper, using optimization methods on Riemannian submanifolds, we establish two
improved inequalities for generalized normalized δ-Casorati curvatures of Lagrangian …

The generalized Wintgen inequality was conjectured by De Smet, Dillen, Verstraelen and
Vrancken in 1999 for submanifolds in real space forms. It is also known as the DDVV …

Using Oprea's optimization methods on submanifolds, we give another proof of the
inequalities relating the normalized δ-Casoraticurvature δ^ c (n− 1) for submanifolds in real …

In the present paper, first we prove some results by using fundamental properties of totally
real statistical submanifolds immersed into holomorphic statistical manifolds. Further, we …

Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms |
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For submanifolds of general dimension and codimension in statistical manifolds of constant
curvature, a sharp inequality of Wintgen type is given by us. It generalizes the inequality …

Generalized Wintgen inequality for slant submanifolds in metallic Riemannian space forms |
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