Scalar curvature pinching for CMC hypersurfaces in a sphere (Q2438004)

Since the appearence of the famous rigidity theorem for minimal submanifolds due to Simons, Lawson and Chern-do Carmo-Kobayashi, various scalar curvature pinching problems for submanifolds have been studied by several geometers. The present paper is devoted to a pinching result for an \(n\)-dimensional closed and CMC hypersurface in \(S^{n+1}\) with \(3\leq n\leq 8\). In this way some previous results on minimal hypersurfaces in spheres are generalized.