Curvatura de Lie das hipersuperfícies de Dupin - VITOR, Erivelton Paulo (2008)
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 Lie sphere geometry. We construct example of a non-compact proper Dupin hypersurface immersed in Sn on which the Lie curvature Ψ = 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 Ψ has a constant value c, 0 < c < 1.