Ricci Curvature for Warped Product Submanifolds of Sasakian Space Forms and Its Applications to Differential Equations

Abstract

In the present paper, we establish a Chen–Ricci inequality for a C-totally real warped product submanifold Mn of Sasakian space forms M2m+1ε. As Chen–Ricci inequality applications, we found the characterization of the base of the warped product Mn via the first eigenvalue of Laplace–Beltrami operator defined on the warping function and a second-order ordinary differential equation. We find the necessary conditions for a base B of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere Sp.