Improved Chen-Ricci inequality for curvature-like tensors and its applications

TL;DR

This paper introduces an improved Chen-Ricci inequality for curvature-like tensors and applies it to study specific submanifolds in complex and Sasakian space forms, advancing geometric inequality understanding.

Contribution

It presents a new, sharper Chen-Ricci inequality for curvature-like tensors and demonstrates its applications to various submanifold classes in complex and Sasakian geometries.

Findings

Derived an improved Chen-Ricci inequality for curvature-like tensors.

Applied the inequality to analyze Lagrangian and Kaehlerian slant submanifolds.

Extended the inequality's application to C-totally real submanifolds in Sasakian space forms.

Abstract

We present Chen-Ricci inequality and improved Chen-Ricci inequality for curvature like tensors. Applying our improved Chen-Ricci inequality we study Lagrangian and Kaehlerian slant submanifolds of complex space forms and C-totally real submanifolds of Sasakian space forms.