Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas

Singular Riemannian foliations in spheres provide local models for an extensive kind of singular Riemannian foliations, whose theory contributes in the understanding of Riemannian manifolds. Hence the importance of studying and classifying them, a research subject that still remains open. In 2014, M...

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Autor Principal: Torres Lozano, Julia Carolina
Formato: Trabajo de grado (Bachelor Thesis)
Lenguaje:Desconocido (Unknown)
Publicado: 2017
Materias:
Acceso en línea:http://babel.banrepcultural.org/cdm/ref/collection/p17054coll23/id/914
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spelling ir-p17054coll23-9142020-09-28 Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas Torres Lozano, Julia Carolina Singular Riemannian foliations in spheres provide local models for an extensive kind of singular Riemannian foliations, whose theory contributes in the understanding of Riemannian manifolds. Hence the importance of studying and classifying them, a research subject that still remains open. In 2014, Marco Radeschi constructed indecomposable singular Riemannian foliations of arbitrary codimension, most of them inhomogeneous, which generalized all known examples of that type so far. The present dissertation is a detailed study of his work, along with observations about the progress made on this dynamic field since that paper was published. Besides introducing preliminary notions and examples on singular Riemannian foliations, isometric actions and Clifford theory, it is explained a construction of inhomogeneous isoparametric hypersurfaces, due to Ferus, Karcher and Mu?nzner, that was a fundamental framework for the results of Radeschi. After that, it is described exhaustively the construction of Clifford and composed foliations in spheres, which are the examples that Radeschi created using Clifford systems. In the sequel it is established an extraordinary bijective correspondence between Clifford foliations (merely geometric objects) and Clifford systems (purely algebraic objects). This text finishes examining the relations of homogeneity properties among FKM, Clifford and composed foliations. Singular Riemannian foliation; Clifford foliation; Composed foliation; FKM foliation; Clifford system; Clifford algebra; Foliación Riemanniana singular; Foliación de Clifford; Foliación compuesta; Foliación FKM; Sistema de Clifford; Álgebra de Clifford Ciencias naturales y matemáticas; Ciencias naturales y matemáticas / Matemáticas 2017 PDF Tesis ENG - Inglés Colfuturo © Derechos reservados del autor http://babel.banrepcultural.org/cdm/ref/collection/p17054coll23/id/914
institution Biblioteca Virtual Banco de la República - Colecciones digitales
collection Custom
language Desconocido (Unknown)
topic Singular Riemannian foliation; Clifford foliation; Composed foliation; FKM foliation; Clifford system; Clifford algebra; Foliación Riemanniana singular; Foliación de Clifford; Foliación compuesta; Foliación FKM; Sistema de Clifford; Álgebra de Clifford
Ciencias naturales y matemáticas; Ciencias naturales y matemáticas / Matemáticas
spellingShingle Singular Riemannian foliation; Clifford foliation; Composed foliation; FKM foliation; Clifford system; Clifford algebra; Foliación Riemanniana singular; Foliación de Clifford; Foliación compuesta; Foliación FKM; Sistema de Clifford; Álgebra de Clifford
Ciencias naturales y matemáticas; Ciencias naturales y matemáticas / Matemáticas
Torres Lozano, Julia Carolina
Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
description Singular Riemannian foliations in spheres provide local models for an extensive kind of singular Riemannian foliations, whose theory contributes in the understanding of Riemannian manifolds. Hence the importance of studying and classifying them, a research subject that still remains open. In 2014, Marco Radeschi constructed indecomposable singular Riemannian foliations of arbitrary codimension, most of them inhomogeneous, which generalized all known examples of that type so far. The present dissertation is a detailed study of his work, along with observations about the progress made on this dynamic field since that paper was published. Besides introducing preliminary notions and examples on singular Riemannian foliations, isometric actions and Clifford theory, it is explained a construction of inhomogeneous isoparametric hypersurfaces, due to Ferus, Karcher and Mu?nzner, that was a fundamental framework for the results of Radeschi. After that, it is described exhaustively the construction of Clifford and composed foliations in spheres, which are the examples that Radeschi created using Clifford systems. In the sequel it is established an extraordinary bijective correspondence between Clifford foliations (merely geometric objects) and Clifford systems (purely algebraic objects). This text finishes examining the relations of homogeneity properties among FKM, Clifford and composed foliations.
format Trabajo de grado (Bachelor Thesis)
author Torres Lozano, Julia Carolina
author_facet Torres Lozano, Julia Carolina
author_sort Torres Lozano, Julia Carolina
title Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
title_short Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
title_full Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
title_fullStr Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
title_full_unstemmed Clifford and composed foliations = Foliaciones de Clifford y foliaciones compuestas
title_sort clifford and composed foliations = foliaciones de clifford y foliaciones compuestas
publishDate 2017
url http://babel.banrepcultural.org/cdm/ref/collection/p17054coll23/id/914
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score 11,489418