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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1132–1156 | Cite as

Minimal Surfaces in \(\mathbb{S}^{2} \times\mathbb{S}^{2}\)

  • Francisco Torralbo
  • Francisco UrbanoEmail author
Article

Abstract

A general study of minimal surfaces of the Riemannian product of two spheres \(\mathbb {S}^{2}\times \mathbb {S}^{2}\) is tackled. We establish a local correspondence between (non-complex) minimal surfaces of \(\mathbb {S}^{2} \times \mathbb {S}^{2}\) and a certain pair of minimal surfaces of the sphere \(\mathbb {S}^{3}\). This correspondence also allows us to link minimal surfaces in \(\mathbb{S}^{3}\) and in the Riemannian product \(\mathbb {S}^{2} \times \mathbb {R}\). Some rigidity results for compact minimal surfaces are also obtained.

Keywords

Surfaces Minimal Complex surfaces 

Mathematics Subject Classification

53C42 53C40 

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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