Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.

Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature

In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.

Pinching Theorems for a Vanishing C-Bochner Curvature Tensor

The main purpose of this article is to construct inequalities between a main intrinsic invariant (the normalized scalar curvature) and an extrinsic invariant (the Casorati curvature) for some submanifolds in a Sasakian manifold with a zero C-Bochner tensor.

Certain inequalities for the Casorati curvatures of submanifolds of generalized (k,μ)-space-forms

The paper deals with the study of Casorati curvature of submanifolds of generalized [Formula: see text]-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.

Lower bounds of generalised normalised δ- Casorati curvature for real hypersurfaces in complex quadric endowed with semi-symmetric metric connection

The main intention of the present paper is to develop two extremal inequalities involving normalized δ-Casorati curvature and extrinsic generalised normalised δ-Casorati curvature for real hypersurfaces in complex quadric Qm admitting semi-symmetric metric connection. Further, we derive the necessary and sufficient condition for the equality in both cases

Some inequalities for submanifolds in a Riemannian manifold of nearly quasi-constant curvature

In this paper, we derive a DDVV-type inequality for submianifolds in a Riemannian manifold of nearly quasi-constant curvature. Moreover, two inequalities involving the Casorati curvature and the scalar curvature are obtained.