The Gauss Map of Minimal Surfaces in the Heisenberg Group

Abstract : We study the Gauss map of minimal surfaces in the Heisenberg group Nil(3) endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane H(2). Conversely, any nowhere antiholomorphic harmonic map into H(2) is the Gauss map of a nowhere vertical minimal surface. Finally, we study the image of the Gauss map of complete nowhere vertical minimal surfaces.
Document type :
Journal articles

https://hal-upec-upem.archives-ouvertes.fr/hal-00693002
Submitted on : Tuesday, May 1, 2012 - 7:23:39 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

Citation

Benoit Daniel. The Gauss Map of Minimal Surfaces in the Heisenberg Group. International Mathematics Research Notices, Oxford University Press (OUP), 2011, ? (3), pp.674--695. ⟨10.1093/imrn/rnq092⟩. ⟨hal-00693002⟩

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