Isothermic nets with spherical parameter lines from discrete holomorphic maps

2024/03/20 by Hoffmann, Tim, Szewieczek, Gudrun · 2 citations
#53A04 #53A70 (Primary) 53A31 #53C12 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.13476

Abstract

We prove that all discrete isothermic nets with a family of planar or spherical lines of curvature can be obtained from special discrete holomorphic maps via lifted-folding. This novel approach is a generalization and discretization of a classical method to create planar curvature lines on smooth surfaces. In particular, this technique provides an efficient way to construct discrete isothermic topological tori composed of fundamental pieces from discrete periodic holomorphic maps.

Cited by

• Discrete Koenigs nets, inscribed quadrics and autoconjugate curves
• Discrete Koenigs nets and finite Laplace sequences

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