We present a method giving a spinorial characterization of an immersion into a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory for such target spaces. We also study special cases: we recover previously known results concerning immersions in \(\mathbb {S}^2\times \mathbb {R}\) and we obtain new spinorial characterizations of immersions in \(\mathbb {S}^2\times \mathbb {R}^2\) and in \(\mathbb {H}^2\times \mathbb {R}.\) We then study the theory of \(H=1/2\) surfaces in \(\mathbb {H}^2\times \mathbb {R}\) using this spinorial approach, obtain new proofs of some of its fundamental results and give a direct relation with the theory of \(H=1/2\) surfaces in \(\mathbb {R}^{1,2}\).

我们提出了一种方法，给出了恒定曲率空间乘积浸没的旋量表征。作为第一个应用，我们使用旋量获得了此类目标空间的沉浸理论基本定理的证明。我们还研究特殊情况：我们恢复了先前已知的有关\(\mathbb {S}^2\times \mathbb {R}\)中浸没的结果，并且我们获得了\(\mathbb {S}^2中浸没的新旋量表征\times \mathbb {R}^2\)和\(\mathbb {H}^2\times \mathbb {R}.\)然后我们研究\(H=1/2\)曲面的理论\ (\mathbb {H}^2\times \mathbb {R}\)使用这种旋量方法，获得其一些基本结果的新证明，并给出与\(H=1/2\)曲面理论的直接关系在\(\mathbb {R}^{1,2}\)中。