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The Gauss map of minimal graphs in the Heisenberg group. (English) Zbl 1268.22006

The geometry of surfaces of the Heisenberg group \(H_3\) endowed with a fixed left-invariant Riemannian metric is studied. The Gauss map for hypersurfaces of any Lie group is defined and the classification of minimal surfaces in \(H_3\) with Gauss maps of ranks zero and one is given. There is a reference list of 17 items.

MSC:

22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
49Q05 Minimal surfaces and optimization
57R40 Embeddings in differential topology
57R42 Immersions in differential topology
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