Global characterizations of the sphere

Stamou, George

doi:10.1090/S0002-9939-1978-0467620-8

Global characterizations of the sphere
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by George Stamou PDF

Proc. Amer. Math. Soc. 68 (1978), 328-330 Request permission

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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