On some inequalities for submanifolds of Bochner Kaehler manifolds

TL;DR

This paper generalizes Chen's inequalities for submanifolds within Bochner Kaehler manifolds, extending known geometric inequalities and establishing new bounds for CR-warped product submanifolds.

Contribution

It introduces generalized inequalities for submanifolds in Bochner Kaehler manifolds and derives a new inequality for scalar curvature of CR-warped product submanifolds.

Findings

Generalized Chen inequalities for submanifolds of Bochner Kaehler manifolds

Established scalar curvature inequality for CR-warped product submanifolds

Extended geometric bounds in complex differential geometry

Abstract

B. Y. Chen established sharp inequalities between certain Riemannian invariants and the squared mean curvature for submanifolds in real space form as well as in complex space form. In this paper we generalize Chen inequalities for submanifolds of Bochner Kaehler manifolds. Moreover, we consider CR-warped product submanifolds of Bochner Kaehler manifold and establish an inequality for scalar curvature.