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Doctoral Thesis
DOI
10.11606/T.45.2018.tde-14122017-130959
Document
Author
Full name
Benigno Oliveira Alves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Silva, Marcos Martins Alexandrino da (President)
Gomes, José Barbosa
Toben, Dirk
Vazquez, Miguel Dominguez
Victoria, Miguel Angel Javaloyes
Title in Portuguese
Sobre folheações Finslerianas singulares
Keywords in Portuguese
Espaços Randers
Folheação Finsleriana singular
Abstract in Portuguese
Nesta tese foi introduzido o conceito de folheação Finsleriana singular, que generaliza ação Finsleriana, submersão Finsler e folheação Finsleriana. O primeiro resultado desta tese afirma que qualquer folheação Finsleriana singular sobre uma variedade Randers com data (h,W) é folheação Riemanniana singular com respeito a h e W é um campo folheado. Para obter este resultado provou-se um teorema de redução ao slice, que permite relacionar uma folheação Finsleriana singular com uma folheação Finsleriana singular em um espaço de Minkowski. O terceiro resultado garante a equifocalidade para as fibras regulares de uma submersão singular analítica que na parte regular é uma submersão Finsleriana. No transcurso do trabalho verificou-se propriedades relevantes das folheações Finslerianas singulares e a existência de vizinhanças tubulares Finslerianas, uma propriedade básica que não estava escrita na literatura.
Title in English
On singular Finsler foliation
Keywords in English
Randers spaces
Singular Finsler foliation
Abstract in English
In this thesis we introduce the concept of singular Finsler foliation, which generalizes the concepts of Finsler actions, Finsler submersions and Finsler foliations. In the first theorem we show that if F is a singular Finsler foliation on a Randers manifold (M,Z) with Zermelo data (h,W), then F is a singular Riemannian foliation on the Riemannian manifold (M, h). In order to prove this theorem we present in the second theorem a slice reduction that relates local singular Finsler foliations on Finsler manifolds with singular Finsler foliations on Minkowski spaces. Finally in the third result we prove the equifocality of the fibers of an analytic singular submersion that is a Finsler submersion in the regular part. Along the work we stress relevant properties on singular Finsler foliations and we also remark the existence of tubular neigborhoods in Finsler geometry, a basic result that we did not find properly written in the literature.
 
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TeseBenigno.pdf (682.58 Kbytes)
Publishing Date
2018-01-24
 
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