Zero mean curvature surfaces in isotropic space with planar curvature lines

TL;DR

This paper classifies zero mean curvature surfaces with planar curvature lines in isotropic 3-space, revealing they form a 1-parameter family and exploring their connection to Thomsen-type affine minimal surfaces.

Contribution

It provides a complete classification of these surfaces and investigates their relationship to Thomsen-type surfaces in isotropic space.

Findings

All such surfaces form a 1-parameter family.

They are related to Thomsen-type affine minimal surfaces.

The classification is comprehensive and complete.

Abstract

We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investigate their relationship to Thomsen-type surfaces in isotropic 3-space, those zero mean curvature surfaces in isotropic 3-space that are also affine minimal.