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On convex hypersurfaces in $E^{n + 1}$

Thomas Hasanis — 1984

Colloquium Mathematicae

Characterizations of the sphere by the curvature of the second fundamental form

Thomas Hasanis — 1982

Colloquium Mathematicae

A new characterization of the sphere in $R^{3}$

Thomas Hasanis — 1980

Annales Polonici Mathematici

Let M be a closed connected surface in $R^{3}$ with positive Gaussian curvature K and let $K_{I} I$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_{I} I = c \sqrt H K^{r}$ , for some constants c and r, where H is the mean curvature of M.

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