Ricci curvature for warped product submanifolds of Sasakian space forms and its applications to differential equations
Summary: In the present paper, we establish a Chen-Ricci inequality for a C-totally real warped product submanifold \(M^n\) of Sasakian space forms \(\mathbb{M}^{2 m + 1}(\varepsilon)\). As Chen-Ricci inequality applications, we found the characterization of the base of the warped product \(M^n\) 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 \(\mathbb{B}\) of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere \(\mathbb{S}^p\).
scientific article; zbMATH DE number 7393925
scientific article