Minimal surfaces with only horizontal symmetries

TL;DR

This paper introduces the first known examples of triply periodic minimal surfaces exhibiting only horizontal symmetries, expanding the understanding of symmetry types in minimal surface theory.

Contribution

It provides the first explicit examples of triply periodic minimal surfaces with exclusively horizontal symmetries, a previously unobserved symmetry configuration.

Findings

First examples of such surfaces discovered

Surfaces exhibit only horizontal symmetries

Advances understanding of symmetry in minimal surfaces

Abstract

We find the first examples of triply periodic minimal surfaces of which the intrinsic symmetries are all of horizontal type.