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

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