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

by Vitor, Erivelton Paulo

Abstract (Summary)
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.
This document abstract is also available in Portuguese.
Bibliographical Information:

Advisor:Luciana Maria Dias de Ávila Rodrigues

School:Universidade Federal de Goiás

School Location:Brazil

Source Type:Master's Thesis

Keywords:Hypersurfaces Dupin Lie curvature geometry

ISBN:

Date of Publication:03/28/2008

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