Maximal translation surfaces in Lorentz-Minkowski space

2025/07/18 by López, Rafael
#53A10 #53C42 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.14103

Abstract

A translation surface in Lorentz-Minkowski space \rr³ is a surface defined as the sum of two spatial curves. In this paper we present a classification of maximal surfaces of translation type. We prove that if a generating curve is planar, then the other generating curve is also planar. We give a full description of these surfaces. In case that both curves are of Frenet type, we generalize the Scherk surfaces. In case that a curve is a pseudo-null curve, we obtain new examples of maximal surfaces which have not counterparts in Euclidean space.

Citations

• Lectures on Minimal Surfaces
• Translation surfaces in Euclidean space with constant Gaussian curvature
• Classifications of translation surfaces in isotropic geometry with constant curvature
• Minimal translation surfaces in hyperbolic space

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