Subvariedades isoparamétricas do espaço Euclidiano / Isoparametric submanifolds of Euclidian space

AUTOR(ES)

Jaime Leonardo Orjuela Chamorro

DATA DE PUBLICAÇÃO

2008

RESUMO

The goal of this dissertation is to present an introduction to the study of isoparametric submanifolds of Euclidean space. We begin with an introduction to the history of the subject. Then we present the basic results of submanifold theory of space forms. We compute the fundamental equations of first and second order, and we prove the fundamental theorem of submanifold theory. Next, we define isoparametric submanifolds and discuss some basic constructions, as curvature normals, Coxeter groups, Weyl chambers and parallel and focal submanifolds. We prove two decomposition theorems about isoprametric submanifolds using techniques that we learnt from [HL97], paper in which the case of submanifolds of Hilbert spaces is studied. Then we prove slice theorem. We also discuss those submanifold from the classical point of view, namely, isoparametric maps. We finish by explaining some examples: isoparametric hipersurfaces of spheres and principal orbits of the adjoint action of a Lie group on its Lie algebra.

ASSUNTO(S)

coxeter groups isoparametric submanifolds grupos de coxeter subvariedades isoparamétricas normal curvatures normais de curvatura principal curvatures curvaturas principais

Documentos Relacionados

• Sobre subvariedades totalmente reais
• Geometry and topology of isoparametric submanifolds in euclidean spaces
• Superfícies de Weingarten Generalizadas do Tipo Rotacional no 3-Espaço Euclidiano
• Superfícies de Weingarten Generalizadas do Tipo Rotacional no 3-Espaço Euclidiano
• Superfícies Helicoidais no espaço Euclidiano e de Minkowski