  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 Spin$^c$ 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 $\mathbb M_1(c_1) \times
\mathbb M_2(c_2)$ ($c_1 \neq c_2$) having a local structure product, are of
constant mean curvature.
