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Results in Mathematics

, 74:147 | Cite as

Equiaffine Isoparametric Functions and Their Regular Level Hypersurfaces

  • Wenjing Hao
  • Xingxiao LiEmail author
Article
  • 62 Downloads

Abstract

In this paper, we aim to introduce and study the (locally strongly convex) equiaffine isoparametric functions on the affine space \(A^{n+1}\), making the emphasis on their relation with the affine isoparametric hypersurfaces. Motivated by the case in the Euclidean space \(E^{n+1}\), we first introduce the concept of equiaffine parallel hypersurfaces in \(A^{n+1}\), and then equivalently re-define the equiaffine isoparametric hypersurfaces to be ones that are among families of equiaffine parallel hypersurfaces in \(A^{n+1}\) of constant affine mean curvature. As the main result, we prove that an equiaffine isoparametric hypersurface is nothing but exactly a regular level set of some equiaffine isoparametric function.

Keywords

Affine isoparametric function affine isoparametric hypersurfaces affine parallel hypersurfaces affine principal curvature affine mean curvature 

Mathematics Subject Classification

Primary 53A15 Secondary 53B25 

Notes

Acknowledgements

The second author thanks Professor A.-M. Li for his constant encouragement.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesHenan Normal UniversityXinxiangPeople’s Republic of China

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