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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Bibliographic Details
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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Summary: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.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-009-9178-4