In this paper, we introduce and study the locally strongly convex equiaffine isoparametric hypersurfaces and equiaffine isoparametric functions on the affine space A n+1 . Motivated by the case on the Euclidean space E n+1 , we first introduce the concept of equiaffine parallel hypersurfaces in A n+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 A n+1 . Finally, we introduce the concept of equiaffine isoparametric functions on A n+1 , and prove that any equiaffine isoparametric hypersurface is exactly a regular level set of some equiaffine isoparametric function.2010 Mathematics Subject Classification. Primary 53A15; Secondary 53B25. Key words and phrases. affine isoparametric function, affine isoparametric hypersurfaces, affine parallel hypersurfaces, affine principal curvature, affine mean curvature.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.