Curvatura de Lie das hipersuperfícies de Dupin Lie curvature of Dupin hypersurfaces

by Vitor, Erivelton Paulo

In this work we study some results from the article of Tomas E. Cecil, On the Lie curvature of Dupin hypersurfaces [4]. We study the basic concepts of Lie sphere geometry, which given the framework for the study of Dupin hypersurfaces in the Liesphere geometry. We construct example of a non-compact proper Dupin hypersurface immersed in Sn on which the Lie curvature amp;#936; = 1/2 which is not Lie equivalent to an open subset of an isoparametric hypersurface in Sn. We also produce example on which Lie curvature amp;#936; has a constant value c, 0 lt; c lt; 1.