# On the umbilic set of immersed surfaces in three-dimensional space forms

created by roncoroni on 21 Oct 2022

[BibTeX]

Accepted Paper

Inserted: 21 oct 2022
Last Updated: 21 oct 2022

Journal: Bull. Sci. Math.
Year: 2020

ArXiv: 1904.08145 PDF

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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