Asymptotic lines on real Milnor links of a family that realizes any genus.

We describe the global foliation of asymptotic lines on compact surfaces of genus greater than one, defined in R 4 as the links of the real part of the Milnor fibration of a family of polynomials. Through this analysis, we present a description of the global foliation of lines of curvature of the embeddings, defined as the images of the stereographic projection of these links into R 3. [ABSTRACT FROM AUTHOR]