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Hypersurfaces with constant scalar curvature in space forms. (English) Zbl 0864.53040
By the study of Cheng-Yau’s self-adjoint operator , 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.

MSC:
53C40Global submanifolds (differential geometry)
53A07Higher-dimensional and -codimensional surfaces in Euclidean n-space
References:
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