An intrinsic rigidity theorem for closed minimal hypersurfaces in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature

2015/07/22 by Bing Tao Tang, Ling Yang, Tang, Bing +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1507.06156

Abstract

Let M be a closed minimal hypersurface in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature. We prove that, if the sum of the cubes of all principal curvatures and the number of distinct principal curvatures are constant, then M is isoparametric. Moreover, We give all possible values for squared length of the second fundamental form of M. This result provides another piece of supporting evidence to the Chern conjecture.

Related

• Rigidity of closed minimal hypersurface in \mathbbS⁵
• Minimal Hypersurfaces with constant scalar curvature in S⁶
• Chern conjecture on minimal hypersurfaces
• Strong Rigidity of Closed Minimal Hypersurfaces in Euclidean Spheres
• Chern's Conjecture in the Dupin case