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

Thomas Hasanis (1980)

Annales Polonici Mathematici

Similarity:

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 ${K}_{I}I=c\surd H{K}^{r}$, for some constants c and r, where H is the mean curvature of M.