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| An Intrinsic Rigidity Theorem for Closed Minimal Hypersurfaces in S5 with Constant Nonnegative Scalar Curvature |
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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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Net amount： 1253 |
Authors： |
Bing TANG; Ling YANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11471078, 11622103). |
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| 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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