The Gauss map of minimal surfaces in Berger spheres

It is proved that a pair of spinors satisfying a Dirac type equation represents surfaces immersed in Berger spheres with prescribed mean curvature. Using this, we prove that the Gauss map of a minimal surface immersed in a Berger sphere is harmonic. Conversely, we exhibit a representation of minimal...

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Published in:Annals of global analysis and geometry 2010-02, Vol.37 (2), p.143-162
Main Authors: de Lira, Jorge H. S., Hinojosa, Jorge A.
Format: Article
Language:English
Subjects:
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Lie groups
Mathematical Physics
Mathematics
Mathematics and Statistics
Original Paper
Spheres
Studies
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Hinojosa, Jorge A.
description It is proved that a pair of spinors satisfying a Dirac type equation represents surfaces immersed in Berger spheres with prescribed mean curvature. Using this, we prove that the Gauss map of a minimal surface immersed in a Berger sphere is harmonic. Conversely, we exhibit a representation of minimal surfaces in Berger spheres in terms of a given harmonic map. The examples we constructed appear in associated families.
doi_str_mv 10.1007/s10455-009-9178-4
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subjects Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Lie groups
Mathematical Physics
Mathematics
Mathematics and Statistics
Original Paper
Spheres
Studies
title The Gauss map of minimal surfaces in Berger spheres
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