Study of Differential Equations on Warped Product Semi-Invariant Submanifolds of the Generalized Sasakian Space Forms

Ibrahim Al-Dayel,Meraj Ali Khan

doi:10.1155/2021/7042949

Abstract

The purpose of the present paper is to study the applications of Ricci curvature inequalities of warped product semi-invariant product submanifolds in terms of some differential equations. More precisely, by analyzing Bochner’s formula on these inequalities, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to Euclidean space. We also look at the effects of certain differential equations on warped product semi-invariant product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

Highlights

Bishop and O’Neill [1] evaluated the geometry of manifolds having negative curvature and noticed that Riemannian product manifolds do have nonnegative curvature
These calculations demonstrated that a nonconstant function λ on a complete Riemannian manifold ðUn, gÞ satisfies the differential equation as follows:
The purpose of this paper is to study the impact of differential equation on warped product semi-invariant product submanifolds in the framework of generalized Sasakian space form

Summary

Introduction

Bishop and O’Neill [1] evaluated the geometry of manifolds having negative curvature and noticed that Riemannian product manifolds do have nonnegative curvature. The approach of differential equations was used by the authors [5, 6] to describe the Euclidean sphere These calculations demonstrated that a nonconstant function λ on a complete Riemannian manifold ðUn, gÞ satisfies the differential equation as follows:. = 0, ð3Þ if and only if there exists a nonconstant function φ : Un ⟶ R with an eigenvalue λ1 < 0, which satisfies the following differential equation: An almost contact metric manifold is said to be nearly Sasakian manifold, if. Ali et al [8] characterized warped product submanifolds in Sasakian space form by the approach of differential equation. The purpose of this paper is to study the impact of differential equation on warped product semi-invariant product submanifolds in the framework of generalized Sasakian space form

Preliminaries

Main Results

Conclusions