Complete hypersurfaces with constant scalar curvature and constant mean curvature in \(R^ 4\) (Q1067621)

Complete hypersurfaces in \(R^ 4\) with constant scalar curvature and constant mean curvature are considered. By using a generalized maximum principle discovered by \textit{S.-T. Yau} [Commun. Pure Appl. Math. 28, 201-228 (1975; Zbl 0291.31002)] and a technique used by \textit{C. Peng} and \textit{C. Terng} [Math. Ann. 266, 105-113 (1983; Zbl 0508.53060)], the author proves the following : Let M be a complete and connected hypersurface in \(R^ 4\), with non-zero constant mean curvature and non- negative scalar curvature \(\tau\). Then \(\tau\) takes on the values \(6H^ 2\), \((9/2)H^ 2\) and 0.