# Laguerre isoparametric and Dupin hypersurfaces in $$\mathbb {R}^n$$ R n

Laguerre isoparametric and Dupin hypersurfaces in $$\mathbb {R}^n$$ R n Let $$x: M \rightarrow \mathbb {R}^n$$ x : M → R n be an $$(n-1)$$ ( n - 1 ) -dimensional umbilic free hypersurface with non-zero principal curvatures in $$\mathbb {R}^n$$ R n , $$\mathbf B$$ B be the Laguerre second fundamental form, $$\mathbf L$$ L be the Laguerre tensor and $${\mathbf D}={\mathbf L}+\lambda {\mathbf B}$$ D = L + λ B be the para-Laguerre tensor of the immersion x, where $$\lambda$$ λ is a constant. In this paper, we study the Laguerre isoparametric hypersurfaces, constant para-Laguerre eigenvalues hypersurfaces and Dupin hypersurfaces in $$\mathbb {R}^n$$ R n and obtain some classification theorems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

# Laguerre isoparametric and Dupin hypersurfaces in $$\mathbb {R}^n$$ R n

, Volume 112 (2) – Feb 27, 2017
12 pages

/lp/springer_journal/laguerre-isoparametric-and-dupin-hypersurfaces-in-mathbb-r-n-r-n-5vIFcH14RL
Publisher
Springer Milan
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0386-7
Publisher site
See Article on Publisher Site

### Abstract

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

### Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Feb 27, 2017

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