G. Catino - A. Roncoroni - L. Vezzoni
On the umbilic set of immersed surfaces in three-dimensional space forms
Accepted Paper
Inserted: 17 apr 2019
Last Updated: 5 nov 2020
Journal: Bull. Sci. Math.
Year: 2020
Abstract:
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated Hopf theorem.
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