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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 879–888 | Cite as

An Intrinsic Rigidity Theorem for Closed Minimal Hypersurfaces in \(\mathbb{S}^5\) with Constant Nonnegative Scalar Curvature

  • Bing Tang
  • Ling Yang
Article
  • 3 Downloads

Abstract

Let M4 be a closed minimal hypersurface in \(\mathbb{S}^5\) with constant nonnegative scalar curvature. Denote by f3 the sum of the cubes of all principal curvatures, by g the number of distinct principal curvatures. It is proved that if both f3 and g are constant, then M4 is isoparametric. Moreover, the authors give all possible values for squared length of the second fundamental form of M4. This result provides another piece of supporting evidence to the Chern conjecture.

Keywords

Chern conjecture Isoparametric hypersurfaces Scalar curvature Minimal hypersurfaces in spheres 

2000 MR Subject Classification

53B25 53C40 

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Notes

Acknowledgement

The first author would like to thank his supervisor Professor Ling Yang for his constant encouragement and help.

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina

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