A characteristic property of the sphere

Koufogiorgos, Themis; Hasanis, Thomas

doi:10.1090/S0002-9939-1977-0487927-7

A characteristic property of the sphere
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Proc. Amer. Math. Soc. 67 (1977), 303-305 Request permission

Abstract:

On an ovaloid S with Gaussian curvature $K > 0$ in Euclidean three-space ${E^3}$, the second fundamental form defines a nondegenerate Riemannian metric with curvature ${K_{{\text {II}}}}$. It is shown that S is a sphere if ${K_{{\text {II}}}} = c{H^s}{K^r}$, where c, s and r are constants, H is the mean curvature of S and $0 \leqslant s \leqslant 1$.

References

A new characterization of the sphere

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