The Gauss map of minimal surfaces in S2 x R

In this work, we consider the model of S(2)xR isometric to R-3\{0}, endowed with a metric conformally equivalent to the Euclidean metric of R-3, and we define a Gauss map for surfaces in this model likewise in the Euclidean 3-space. We show as a main result that any two minimal conformal immersions in S(2)x R with the same non-constant Gauss map differ by only two types of ambient isometries: either f = (Id, T), where T is a translation on R, or f=(A,T), where A denotes the antipodal map on S-2. This means that any minimal immersion is determined by its conformal structure and its Gauss map, up to those isometries.