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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Detalles Bibliográficos
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
Descripción
Sumario: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.