Abstract: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 hyper… Show more
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