A new characterization of the sphere in $R^3$
Volume 38 / 1980
Annales Polonici Mathematici 38 (1980), 47-49
DOI: 10.4064/ap-38-1-47-49
Abstract
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.
