# Lines of curvature of the double torus

## TL;DR

This paper analyzes the lines of curvature on a double torus embedded in four-dimensional space, providing a complete foliation description via stereographic projection of a specific polynomial link.

## Contribution

It offers a detailed description of the lines of curvature on a double torus in $\,\mathbb R^4$, linking algebraic and geometric properties of the embedding.

## Key findings

- Complete foliation of lines of curvature described
- Connection between polynomial links and curvature lines established
- Visualization via stereographic projection achieved

## Abstract

We describe the $\nu$-lines of curvature of an embedding of the double torus into $\mathbb R^4$, defined as the link of the real part of the Milnor fibration of a polynomial, where $\nu$ is its gradient. Through this analysis, we present a complete description of the foliation of lines of curvature of the embedding, defined as the image of the stereographic projection of this link into $\mathbb R^3$.