We show by an elementary argument that the second fundamental form of a connected, totally umbilical hypersurface of class C2 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.
On C^2 Umbilical Hypersurfaces / Mantegazza, Carlo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - 150:4(2022), pp. 1745-1748. [10.1090/proc/15804]
On C^2 Umbilical Hypersurfaces
carlo mantegazza
2022
Abstract
We show by an elementary argument that the second fundamental form of a connected, totally umbilical hypersurface of class C2 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.File in questo prodotto:
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