Hypersurfaces with constant scalar curvature in space forms. (English) Zbl 0864.53040

By the study of Cheng-Yau’s self-adjoint operator \(\square\), we prove two rigidity theorems for \(n\)-dimensional hypersurfaces with constant scalar curvature in the \((n+1)\)-dimensional unit sphere \(S^{n+1}\) and in \((n+1)\)-dimensional Euclidean space \(E^{n+1}\), respectively.


53C40 Global submanifolds
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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