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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.

##### MSC:
 53C40 Global submanifolds (differential geometry) 53A07 Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
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##### References:
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