Willmore submanifolds in the unit sphere via isoparametric functions

2014/08/01 by Yuquan Xie, Xie, Yuquan
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1408.0071

openalex publication_date 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore.

Citations

• Moebius geometry of submanifolds in 𝕊 n

Related

• New examples of Willmore submanifolds in the unit sphere via isoparametric functions
• Willmore submanifolds in a sphere
• On focal submanifolds of isoparametric hypersurfaces and Simons formula
• Isoparametric foliation and a problem of Besse on generalizations of Einstein condition
• Control of the isoperimetric deficit by the Willmore deficit