Spinors and isometric immersions of surfaces in 4-dimensional products

Abstract

We prove a spinorial characterization of surfaces isometrically immersed into the $4$-dimensional product spaces $\mathbb{M}^3(c)\times{\mathbb R}$ and $\mathbb{M}^2(c)\times{\mathbb R}^2$, where $\mathbb{M}^n(c)$ is the $n$-dimensional real space form of curvature $c$.