Isometric deformations of isotropic surfaces

2015/07/07 by Marcos Dajczer, M. Dajczer, Theodoros Vlachos +3
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1507.01907

openalex publication_date 2015/07/07 · arxiv created 2015/07/14 · arxiv updated 2015/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It was shown by Ramanathan \citeR that any compact oriented non-simply-connected minimal surface in the three-dimensional round sphere admits at most a finite set of pairwise noncongruent minimal isometric immersions. Here we show that this result extends to isotropic surfaces in spheres of arbitrary dimension. The case of non-compact isotropic surfaces in space forms is also addressed.

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• Surfaces of constant principal-curvatures ratio in isotropic geometry