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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 $\square$, 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.

53C40Global submanifolds (differential geometry)
53A07Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
Full Text: DOI EuDML
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