Minimal translation surfaces in Sol₃

2010/10/06 by López, Rafael, Munteanu, Marian Ioan · 2 citations
#53B25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.1085

Abstract

In the homogeneous space Sol₃, a translation surface is parameterized by x(s,t)=α(s)∗β(t), where α and β are curves contained in coordinate planes and ∗ denotes the group operation of Sol₃. In this paper we study translation surfaces in Sol₃ whose mean curvature vanishes.

Cited by

• Classification of Minimal Surfaces and Solitons to the Mean Curvature Flow in ℍ³ as Translation Surfaces
• Rigidity of Translation Surfaces in the Three-Dimensional Sphere \mathbbS³

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