| Summary: | In this work, we consider the model of S2×R isometric to R3\ { 0 } , endowed with a metric conformally equivalent to the Euclidean metric of R3, 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 S2×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 S2. This means that any minimal immersion is determined by its conformal structure and its Gauss map, up to those isometries. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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