Reflection principles for zero mean curvature surfaces in the simply isotropic 3-space

2022/07/06 by Akamine, Shintaro, Fujino, Hiroki
#31A05 #31A20 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53B30

paper · doi:10.48550/arxiv.2207.02450

Abstract

Zero mean curvature surfaces in the simply isotropic 3-space \mathbbI³ naturally appear as intermediate geometry between geometry of minimal surfaces in 𝔼³ and that of maximal surfaces in \mathbbL³. In this paper, we investigate reflection principles for zero mean curvature surfaces in \mathbbI³ as with the above surfaces in 𝔼³ and \mathbbL³. In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in \mathbbI³, along which the induced metrics become singular.

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