Linear Weingarten hypersurfaces in a unit sphere

Document Type : Research Paper


Southeast University, 210096, Nanjing, P. R. China


In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {\em Math. Ann.} {305} (1996), 665--672].


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