The base of warped product submanifolds of Sasakian space forms characterized by differential equations

Abstract

Abstract In the present paper, we find some characterization theorems. Under certain pinching conditions on the warping function satisfying some differential equation, we show that the base of warped product submanifolds of a Sasakian space form M ˜ 2 m + 1 ( ϵ ) $\widetilde{M}^{2m+1}(\epsilon )$ is isometric either to a Euclidean space R n $\mathbb{R}^{n}$ or a warped product of a complete manifold N and the Euclidean line R $\mathbb{R}$ .

Keywords

• C-totally real warped products
• Sasakian space forms
• Ordinary differential equation
• Isometric immersions