2018/03/28 by Xingxiao Li, Li, Xingxiao, Wenjing Hao +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Primary 53A15 #Secondary 53B25
paper · pdf · doi:10.48550/arxiv.1803.10517
openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce and study the locally strongly convex equiaffine isoparametric hypersurfaces and equiaffine isoparametric functions on the affine space An+1. Motivated by the case on the Euclidean space En+1, we first introduce the concept of equiaffine parallel hypersurfaces in An+1, obtaining some fundamental identities with the basic equiaffine geometric invariants, and then we define the equiaffine isoparametric hypersurfaces to be ones that are among families of equiaffine parallel hypersurfaces of constant affine mean curvature in An+1. Finally, we introduce the concept of equiaffine isoparametric functions on An+1, and prove that any equiaffine isoparametric hypersurface is exactly a regular level set of some equiaffine isoparametric function.