Two characteristic properties of the sphere
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- by Dimitri Koutroufiotis PDF
- Proc. Amer. Math. Soc. 44 (1974), 176-178 Request permission
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
Additional Information
- © Copyright 1974 American Mathematical Society
- 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