Ricci Curvature Inequalities for Skew CR-Warped Product Submanifolds in Complex Space Forms

Meraj Ali Khan,Ibrahim Aldayel

doi:10.3390/math8081317

Meraj Ali Khan, Ibrahim Aldayel

Open Access

https://doi.org/10.3390/math8081317

Copy DOI

Abstract

The fundamental goal of this study was to achieve the Ricci curvature inequalities for a skew CR-warped product (SCR W-P) submanifold isometrically immersed in a complex space form (CSF) in the expressions of the squared norm of mean curvature vector and warping functions (W-F). The equality cases were likewise examined. In particular, we also derived Ricci curvature inequalities for CR-warped product (CR W-P) submanifolds. To sustain this study, an example of these submanifolds is provided.

Highlights

There have been several studies in the past to demonstrate the geometries of submanifolds in the settings of almost Hermitian (A-H) and almost contact metric (A-C M) manifolds
In the literature it was found that Ricci curvature for these warped product submanifolds in complex space forms has not been studied
In this study our point is to establish a connection between Ricci curvature and squared mean curvature for skew CR-warped product (SCR warped product (W-P)) submanifolds in the setting of complex space forms

Summary

Introduction

There have been several studies in the past to demonstrate the geometries of submanifolds in the settings of almost Hermitian (A-H) and almost contact metric (A-C M) manifolds. Theorem 1 was generalized for semi-slant submanifolds in Sasakian space form by Cioroboiu and. W. Yoon [21] studied Chen Ricci inequality for slant submanifols in the framework of cosymplectic space forms. Ali et al [24] generalized Chen Ricci inequality for warped product submanifolds in spheres and provided some applications in mechanics and mathematical physics. In the literature it was found that Ricci curvature for these warped product submanifolds in complex space forms has not been studied. We can say that Theorem 1 is an open problem for skew CR-warped product submanifolds in the setting of complex space forms. In this study our point is to establish a connection between Ricci curvature and squared mean curvature for SCR W-P submanifolds in the setting of complex space forms

Preliminaries

Skew CR-Warped Product Submanifolds

Ricci Curvature for Skew CR-Warped Product Submanifold

Conclusions