2010/03/01 by Jianquan Ge, Ge, Jianquan, Zizhou Tang +1 · 3 citations
Mathematics · #53C20 #57R60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1003.0355
openalex publication_date 2010/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first part of the paper is to improve the fundamental theory of isoparametric functions on general Riemannian manifolds. Next we focus our attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and the Gromoll-Meyer sphere. In particular, as one of main results we prove: there exists no properly transnormal function on any exotic 4-sphere if it exists. Furthermore, by projecting an S3-invariant isoparametric function on Sp(2), we construct a properly transnormal but not an isoparametric function on the Gromoll-Meyer sphere with two points as the focal varieties.