Euclidean hypersurfaces with isometric Gauss maps (Q1056925)

Two isometric immersions of a Riemannian manifold \(M^ n\) into Euclidean space \({\mathbb{R}}^{n+p}\) have isometric Gauss maps if their graphs induce the same metric. Here, we classify such immersions, up to congruence, and their Gauss maps for codimension \(p=1\). They turn out to be associated minimal hypersurfaces. Their Gauss images are associated minimal surfaces in \(S^ n\) which are congruent iff \(M^ n\) is Kähler.