On Algebraic-Geometry Approach to Ribaucour Transformations

TL;DR

This paper introduces an algebraic-geometry framework to construct and analyze Ribaucour transformations of orthogonal nets in differential geometry, providing a new algebraic perspective on classical geometric transformations.

Contribution

It develops an algebraic-geometry approach to generate and study Ribaucour transformations of orthogonal nets, linking algebraic data with geometric transformations.

Findings

Constructed smooth orthogonal nets via algebraic-geometric data.

Established Ribaucour transformations as algebraic-geometric objects.

Provided a new method to analyze classical differential geometry problems.

Abstract

We develop the idea of using an algebraic-geometry approach to classical differential geometry problems. Consider an orthogonal net constructed according to algebraic-geometric data we obtain a set of smooth orthogonal nets that are Ribaucour transformations of the initial orthogonal net.