Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn

  • Shu, Shichang (School of Mathematics and Information Science Xianyang Normal University) ;
  • Li, Yanyan (School of Mathematics and Information Science Xianyang Normal University)
  • Received : 2011.05.22
  • Published : 2013.11.30
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Abstract

Let x : $M{\rightarrow}\mathbb{R}^n$ be an n - 1-dimensional hypersurface in $\mathbb{R}^n$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $D=L+{\lambda}B$ be the Laguerre para-Blaschke tensor of the immersion x, where ${\lambda}$ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para-Blaschke isoparametric hypersurfaces in $\mathbb{R}^n$ with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.

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References

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