An Intrinsic Rigidity Theorem for Closed Minimal Hypersurfaces in S5 with Constant Nonnegative Scalar Curvature

Citation:

Bing TANG,Ling YANG.An Intrinsic Rigidity Theorem for Closed Minimal Hypersurfaces in S5 with Constant Nonnegative Scalar Curvature[J].Chinese Annals of Mathematics B,2018,39(5):879~888
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Authors:

Bing TANG; Ling YANG

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11471078, 11622103).
Abstract: Let $M^4$ be a closed minimal hypersurface in $\mathbb{S}^5$ with constant nonnegative scalar curvature. Denote by $f_3$ the sum of the cubes of all principal curvatures, by $g$ the number of distinct principal curvatures. It is proved that if both $f_3$ and $g$ are constant, then $M^4$ is isoparametric. Moreover, the authors give all possible values for squared length of the second fundamental form of $M^4$. This result provides another piece of supporting evidence to the Chern conjecture.

Keywords:

Chern conjecture, Isoparametric hypersurfaces, Scalar curvature, Minimal hypersurfaces in spheres

Classification:

53B25, 53C40
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