Short Note
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Inserted: 22 apr 2021
Last Updated: 9 nov 2026
Year: 2021
Abstract:
We show by an elementary argument that the second fundamental form of a connected, totally umbilical hypersurface of class $C^2$ is a constant multiple of the metric tensor. It follows that the hypersurface is smooth and it is either a piece of a hyperplane or of a sphere.
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