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Complete space-like hypersurfaces with constant scalar curvature

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Let M n be a complete space-like hypersurface with constant normalized scalar curvature R in the de Sitter space S n + 1 1 and denote . We prove that if the norm square of the second fundamental form of M n satisfies , then either and M n is a totally umbilical hypersurface; or , and, up to rigid motion, M n is a hyperbolic cylinder .

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Received: 8 February 2001 / Revised version: 27 April 2001

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Liu, X. Complete space-like hypersurfaces with constant scalar curvature. manuscripta math. 105, 367–377 (2001). https://doi.org/10.1007/s002290100187

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  • DOI: https://doi.org/10.1007/s002290100187

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