A comment on full discretized isothermic tori in Euclidean spaces

TL;DR

This paper discusses the construction of discrete and semi-discrete isothermic tori in Euclidean spaces using discretized orthogonal systems and Darboux transformations, expanding the understanding of these geometric structures.

Contribution

It introduces a method to generate full discretized and semi-discretized isothermic tori in n-dimensional Euclidean space for any natural dimensions k and n, using Darboux transformations.

Findings

Constructed discrete isothermic tori in Euclidean spaces.

Extended the theory to semi-discrete cases.

Provided a framework for higher-dimensional isothermic tori.

Abstract

Using discretized orthogonal systems (curvature line systems) with periodicity, created using Darboux transformations and their permutability, we have discrete and semi-discrete k-dimensional isothermic tori which are full in n-dimensional Euclidean space, for any natural numbers k between 2 nd n.