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In the present paper, we establish a ChenâRicci inequality for a C-totally real warped product submanifold of Sasakian space forms . As ChenâRicci inequality applications, we found the characterization of the base of the warped product via the first eigenvalue of LaplaceâBeltrami operator defined on the warping function and a second-order ordinary differential equation. We find the necessary conditions for a base of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere .

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