Laguerre characterizations of hypersurfaces in Rn
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Let x : M → Rn be an n − 1-dimensional hypersurface in Rn, L be the Laguerre Blaschke tensor, B be the Laguerre second fun- damental form and D = L + λB be the Laguerre para-Blaschke tensor of the immersion x, where λ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para- Blaschke isoparametric hypersurfaces in Rn with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.
Abstract
Let x : M → Rn be an n − 1-dimensional hypersurface in Rn, L be the Laguerre Blaschke tensor, B be the Laguerre second fun- damental form and D = L + λB be the Laguerre para-Blaschke tensor of the immersion x, where λ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para- Blaschke isoparametric hypersurfaces in Rn with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.
참고문헌 (7)
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- E. Musso, "Laguerre geometry of surfaces with plane lines of curvature", Abh. Math. Sem. Univ. Hamburg, 69, pp.123~138 (1999)