Simple and explicit constructions of semi-discrete surfaces and discrete surfaces

TL;DR

This paper presents straightforward methods to construct semi-discrete and discrete K-surfaces using Jacobi elliptic functions, providing explicit formulas and analyzing their periodic properties.

Contribution

It introduces simple, explicit constructions of semi-discrete and discrete surfaces with detailed periodicity analysis, advancing geometric surface theory.

Findings

Explicit formulas for semi-discrete surfaces

Explicit formulas for discrete K-surfaces

Periodicities of the constructed surfaces

Abstract

We give a simple and explicit constructions of various semi-discrete surfaces and discrete $K$-surfaces in terms of the Jacobi elliptic functions using $\tau$-functions. Their periodicities are also determined.