Abstract: In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by asing the relationship between the square of the length of the second fundamental form and the mean curvature.We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval. This improved the relative results of M.Okumura,ShenYibihg and Sun Ziqi,etc.

Key words:  , totally umbilical, second fundamental form, mean cur ature ,