Geodesic
A new characterization of the sphere in $R^3$
Annales Polonici Mathematici, Tome 38 (1980) no. 1, pp. 47-49

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Let M be a closed connected surface in $R^3$ with positive Gaussian curvature K and let $K_II$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_II = c√HK^r$, for some constants c and r, where H is the mean curvature of M.
DOI : 10.4064/ap-38-1-47-49

Thomas Hasanis 1

1 
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Thomas Hasanis. A new characterization of the sphere in $R^3$. Annales Polonici Mathematici, Tome 38 (1980) no. 1, pp. 47-49. doi: 10.4064/ap-38-1-47-49

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