In the present paper, we establish a Chen–Ricci inequality for a C-totally real warped product submanifold of Sasakian space forms . As Chen–Ricci inequality applications, we found the characterization of the base of the warped product 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 of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere .

中文翻译：

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Sasakian空间形式的翘积子流形的Ricci曲率及其在微分方程中的应用

在本文中，我们为Sasakian空间形式的C个完全真实的扭曲乘积子流形建立了Chen-Ricci不等式。在Chen–Ricci不等式的应用中，我们通过变形函数上定义的Laplace–Beltrami算符的第一特征值和二阶常微分方程，找到了变形积基的特征。我们找到了一个C完全实变形的子流形的底座与欧几里得球等距的必要条件。