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On the Chern conjecture for isoparametric hypersurfaces |
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| Authors: | Tang Zizhou Yan Wenjiao |
| Institution: | 1.Chern Institute of Mathematics, Nankai University, Tianjin, 300071, China ;2.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, China ; |
| Abstract: | For a closed hypersurface Mn ⊂ Sn+1(1) with constant mean curvature and constant non-negative scalar curvature, we show that if \({\rm{tr}}\left({{{\cal A}^k}} \right)\) are constants for k = 3, …, n − 1 and the shape operator \({\cal A}\) then M is isoparametric. The result generalizes the theorem of de Almeida and Brito (1990) for n = 3 to any dimension n, strongly supporting the Chern conjecture. |
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