Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

G. Catino - A. Roncoroni - L. Vezzoni

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

created by roncoroni on 21 Oct 2022
modified by catino on 17 Oct 2023


Published Paper

Inserted: 21 oct 2022
Last Updated: 17 oct 2023

Journal: Bull. Sci. Math.
Year: 2020

ArXiv: 1904.08145 PDF


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.

Credits | Cookie policy | HTML 5 | CSS 2.1