Lines of Curvature on the Double Torus

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 $\mathbb R^3$.