Isometric deformations of minimal surfaces in S⁴

2012/02/29 by Theodoros Vlachos, Vlachos, Theodoros
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1202.6503

arxiv created 2012/02/29 · arxiv updated 2012/03/01

Abstract

We consider the isometric deformation problem for oriented non simply connected immersed minimal surfaces f:M → S⁴. We prove that the space of all isometric minimal immersions of M into S⁴ with the same normal curvature function is, within congruences, either finite or a circle. Furthermore, we show that for any compact immersed minimal surface in S⁴ with nontrivial normal bundle there are at most finitely many noncongruent immersed minimal surfaces in S⁴ isometric to it with the same normal curvature function.

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