The Riemannian product \({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)\), where \({\mathbb{M}}_i(c_i)\) denotes the 2-dimensional space form of constant sectional curvature \(c_i \in {\mathbb{R}}\), has two different \({\mathrm{Spin}^{\mathrm{c}}}\) structures carrying each a parallel spinor. The restriction of these two parallel spinor fields to a 3-dimensional hypersurface M characterizes the isometric immersion of M into \({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)\). As an application, we prove that totally umbilical hypersurfaces of \({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_1(c_1)\) and totally umbilical hypersurfaces of \({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)\) (\(c_1 \ne c_2\)) having a local structure product are of constant mean curvature.

黎曼乘积\({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)\)，其中\({\mathbb{M}}}_i(c_i)\)表示等截面曲率的二维空间形式\(c_i \in {\mathbb{R}}\)，有两个不同的\({\mathrm{Spin}^{\mathrm{c}}}\)结构，每个结构携带一个平行自旋。这两条平行的旋量字段的3维超曲面的限制中号表征的等距浸入中号到\（{\ mathbb {M}} _ 1（c_1）为\倍{\ mathbb {M}} _ 2（C_2）\） . 作为一个应用，我们证明了\({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_1(c_1)\) 的完全脐超曲面和\({\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)\) ( \(c_1 \ne c_2\) ) 具有局部结构积具有恒定的平均曲率。