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Proceedings of the American Mathematical Society

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

 
 

 

Two characteristic properties of the sphere


Author: Dimitri Koutroufiotis
Journal: Proc. Amer. Math. Soc. 44 (1974), 176-178
MSC: Primary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1974-0339025-8
MathSciNet review: 0339025
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Abstract: Let $ S$ be a closed, convex surface in $ {E^3}$ with positive Gaussian curvature $ K$ and let $ {K_{{\text{II}}}}$ be the curvature of its second fundamental form. It is shown that $ S$ is a sphere if $ {K_{{\text{II}}}} \equiv cK$ for some constant $ c$ or if $ {K_{{\text{II}}}} \equiv \surd K$.


References [Enhancements On Off] (What's this?)

  • [1] R. Schneider, Closed convex hypersurfaces with second fundamental form of constant curvature, Proc. Amer. Math. Soc. 35 (1972), 230-233. MR 0307133 (46:6254)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0339025-8
Keywords: Ovaloid, curvature of the second fundamental form, sphere
Article copyright: © Copyright 1974 American Mathematical Society

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