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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global characterizations of the sphere


Author: George Stamou
Journal: Proc. Amer. Math. Soc. 68 (1978), 328-330
MSC: Primary 53C45
MathSciNet review: 0467620
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Abstract: Let S be an ovaloid in Euclidean three-space $ {E^3}$ with Gaussian curvature $ K > 0$ and let $ {K_{{\text{II}}}}$ be the curvature of the second fundamental form II of S. We give some global characterizations of the sphere by the curvature $ {K_{{\text{II}}}}$ which generalize some results of R. Schneider [4], D. Koutroufiotis [2] and the well-known ``H-Satz'' theorem of H. Liebmann.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0467620-8
PII: S 0002-9939(1978)0467620-8
Keywords: Ovaloid, curvature of the second fundamental form, sphere
Article copyright: © Copyright 1978 American Mathematical Society