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Session S39 - Differential Equations and Geometric Structures

Tuesday, July 13, 15:00 ~ 15:50 UTC-3

Curvature lines of compact surfaces of genus $k$.

Federico Sánchez-Bringas

Universidad Nacional Autónoma de México, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We analyze the curvature lines of a compact surface of genus $k \in \mathbb N$ embedded in $\mathbb S^3$ as the link of the real part of the Milnor fibration of a polynomial in $\mathbb C^2$. Since the polynomial is quasi-homogeneous, the link gives rise, under the natural $\mathbb C^*$-action, a family of diffeomorphic surfaces with equivalent curvature lines. We use the symmetries of the model to describe the curvature lines in the cases of genus $k=2,3$. Finally, we study a bifurcation of the case of genus $k=3$ along the umbilic points.

Joint work with Vinicio Gómez Gutiérrez (Universidad Nacional Autónoma de México).

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