Totally umbilic hypersurfaces
Let M be a complete hypersurface with constant mean curvature of a space form of index s \((=0\) or 1). A sufficient condition, which is established between the length of the second fundamental form and the mean curvature, is given for M to be totally umbilical. This result generalizes the reviewer's result [Proc. Am. Math. Soc. 81, 447-450 (1981; Zbl 0461.53032)].
scientific article; zbMATH DE number 4169608