LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn

Title & Authors
LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn
Shu, Shichang; Li, Yanyan;

Abstract
Let x : $\small{M{\rightarrow}\mathbb{R}^n}$ be an n - 1-dimensional hypersurface in $\small{\mathbb{R}^n}$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $D Keywords Laguerre characterization;Laguerre form;Laguerre Blaschke tensor;Laguerre second fundamental form; Language English Cited by References 1. W. Blaschke, Vorlesungenuber Differential geometrie, Springer, Berlin, Heidelberg, New York, Vol. 3, 1929. 2. G. H. Li, Mobius hypersurfaces in$S^{n+1}$with three distinct principal curvatures, J. Geom. 80 (2004), no. 1-2, 154-165. 3. T. Z. Li, Laguerre geometry of surfaces in$\mathbb{R}^3$, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 6, 1525-1534. 4. T. Z. Li, H. Z. Li, and C. P. Wang, Classification of hypersurfaces with parallel Laguerre second fundamental form in$\mathbb{R}^n$, Differential Geom. Appl. 28 (2010), no. 2, 148-157. 5. T. Z. Li and C. P. Wang, Laguerre geometry of hypersurfaces in$\mathbb{R}^n\$, Manuscripta Math. 122 (2007), no. 1, 73-95.

6.
E. Musso and L. Nicolodi, A variational problem for surfaces in Laguerre geometry, Trans. Amer. Math. Soc. 348 (1996), no. 11, 4321-4337.

7.
E. Musso and L. Nicolodi, Laguerre geometry of surfaces with plane lines of curvature, Abh. Math. Sem. Univ. Hamburg 69 (1999), 123-138.