Laguerre isoparametric and Dupin hypersurfaces in \(\mathbb {R}^n\)

Original Paper


Let \(x: M \rightarrow \mathbb {R}^n\) be an \((n-1)\)-dimensional umbilic free hypersurface with non-zero principal curvatures in \(\mathbb {R}^n\), \(\mathbf B\) be the Laguerre second fundamental form, \(\mathbf L\) be the Laguerre tensor and \({\mathbf D}={\mathbf L}+\lambda {\mathbf B}\) be the para-Laguerre tensor of the immersion x, where \(\lambda \) is a constant. In this paper, we study the Laguerre isoparametric hypersurfaces, constant para-Laguerre eigenvalues hypersurfaces and Dupin hypersurfaces in \(\mathbb {R}^n\) and obtain some classification theorems.


Laguerre second fundamental form Laguerre tensor Para-Laguerre tensor Isoparametric Dupin hypersurface 

Mathematics Subject Classification

53A40 53B25 



The author would like to thank the referee for his / her many valuable comments and suggestions that really improve the paper.


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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceXianyang Normal UniversityXianyangPeople’s Republic of China

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