Application of Differential Equations on the Ricci Curvature of Contact CR-Warped Product Submanifolds of S2n+1(1) with Semi-Symmetric Metric Connection

In this paper, we explore the uses of Obata’s differential equation in relation to the Ricci curvature of an odd-dimensional sphere that possesses a semi-symmetric metric connection. Specifically, we establish that, given certain conditions, the underlying submanifold can be identified as an isometric sphere. Additionally, we investigate the impact of specific differential equations on these submanifolds and demonstrate that, when certain geometric conditions are met, the base submanifold can be characterized as a special type of warped product.