Weierstrass-type representations

TL;DR

This paper unifies various Weierstrass-type surface representations using classical transformation theory of Ω-surfaces, enhancing understanding of surfaces with special curvature properties.

Contribution

It provides a unified framework for Weierstrass-type representations through classical transformation theory of Ω-surfaces, connecting different approaches.

Findings

Unified description of Weierstrass-type representations

Connection between surface theory and classical transformation theory

Enhanced methods for constructing surfaces with special curvature

Abstract

Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation theory of $\Omega$-surfaces.