Document Type

Article

Publication Date

10-19-2022

Department

Mathematics

Abstract

This is a survey of local and global classification results concerning Dupin hypersurfaces in Sn (or Rn) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of Sn (or Rn), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

Comments

Link to ArXiv version: https://arxiv.org/abs/2210.10569

AMS Classification numbers: 53A07, 53A40, 53B25, 53C40, 53C42

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.