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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 $\mathbb{R}$ .

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