On the umbilic set of immersed surfaces in three-dimensional space forms
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.08145
- arXiv:
- arXiv:1904.08145
- Bibcode:
- 2019arXiv190408145C
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- Bull. Sci. Mat. 165 (2020), 102917