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Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 143–162 | Cite as

The Gauss map of minimal surfaces in Berger spheres

  • Jorge H. S. de LiraEmail author
  • Jorge A. Hinojosa
Original Paper

Abstract

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.

Keywords

Berger spheres Minimal surfaces Harmonic maps 

Mathematics Subject Classification (2000)

53C42 53C43 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal do CearáFortalezaBrazil
  2. 2.Universidade Federal Rural de Pernambuco, R. Dom Manuel de MedeirosRecifeBrazil

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