Minimal surfaces in S²xS²

2013/01/08 by Francisco Torralbo, Torralbo, Francisco, Francisco Urbano +1
Mathematics · #53C42 (Primary) 53C40 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C40 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1301.1580

25 pages

arxiv created 2013/01/08 · arxiv updated 2013/01/09

Abstract

A general study of minimal surfaces of the Riemannian product of two spheres S²xS² is tackled. We stablish a local correspondence between (non-complex) minimal surfaces of S²xS² and certain pair of minimal surfaces of the sphere S³. This correspondence also allows us to link minimal surfaces in S³ and in the Riemannian product S²xR. Some rigidity results for compact minimal surfaces are also obtained.

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