## 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

### Keywords:

Heisenberg group; minimal surfaces; Gauss map
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