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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Closed convex hypersurfaces with second fundamental form of constant curvature


Author: Rolf Schneider
Journal: Proc. Amer. Math. Soc. 35 (1972), 230-233
MSC: Primary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1972-0307133-1
MathSciNet review: 0307133
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Abstract: It is shown that the Euclidean spheres are the only closed hypersurfaces in Euclidean space on which the second fundamental form defines a (nondegenerate) Riemannian metric of constant curvature.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0307133-1
Keywords: Second fundamental form, closed convex hypersurface, Riemannian metric of constant curvature, scalar curvature, Euclidean sphere
Article copyright: © Copyright 1972 American Mathematical Society