Closed minimal hypersurfaces in \mathbb S⁵ with constant S and A₃

2025/03/29 by Joel Spruck, Ling Xiao, Spruck, Joel +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2503.23194

openalex publication_date 2025/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that a closed minimally immersed hypersurface M⁴⊂\mathbb S⁵ with constant S:=∑_i=1⁴λ_i² and A₃:=∑_i=1⁴λ_i³ whose scalar curvature R_M is nonnegative must be isoparametric. Moreover, S can only be 0, 4, and 12. That is M⁴ is either an equatorial 4-sphere, a clifford torus, or a Cartan's minimal hypersurface.

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