Ros, Antonio Compact hypersurfaces with constant scalar curvature and a congruence theorem. (English) Zbl 0638.53051 J. Differ. Geom. 27, No. 2, 215-220 (1988). Using integral formulas the following main results are shown which generalize classical congruence theorems: a) The sphere is the only compact hypersurface with constant scalar curvature embedded in the Euclidean space. b) Let \(\psi\) : \(M^ n\to {\mathbb{R}}^{n+1}\) be a compact hypersurface embedded in the Euclidean \((n+1)\)-space. Let \(\psi\) ’: \(M^ n\to {\mathbb{R}}^{n+m}\) be an isometric immersion. If the mean curvature vector H’ of \(\psi\) ’ satisfies \(| H'| \leq H\) everywhere (H denoting the mean curvature of \(\psi)\), then \(\psi\) ’ differs from \(\psi\) by a rigid motion. Reviewer: Bernd Wegner Cited in 8 ReviewsCited in 40 Documents MSC: 53C40 Global submanifolds Keywords:integral formulas; congruence theorems; constant scalar curvature; hypersurface; mean curvature vector Citations:Zbl 0638.53052 PDFBibTeX XMLCite \textit{A. Ros}, J. Differ. Geom. 27, No. 2, 215--220 (1988; Zbl 0638.53051) Full Text: DOI