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Contact foliations: closed leaves and generalised Weinstein conjectures

Barbosa, Douglas Luiz Finamore

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação 2023-03-10

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  • Título:
    Contact foliations: closed leaves and generalised Weinstein conjectures
  • Autor: Barbosa, Douglas Luiz Finamore
  • Orientador: Apaza, Carlos Alberto Maquera
  • Assuntos: Ações De Grupos; Dinâmica De Contato; Estruturas De Contato Generalizadas; Folheações; Contact Dynamics; Foliations; Generalised Contact Structures; Group Actions
  • Notas: Tese (Doutorado)
  • Descrição: The Weinstein conjecture, which regards the existence of periodic orbits for Reeb flows, is a classic problem in Contact Geometry. In his doctoral dissertation, Almeida (ALMEIDA, 2018) introduced a novel geometric structure, which generalises contact structures and provides a notion of contact foliation, i.e., higher dimensional analogues for the Reeb flow. In this work, inspired by the classical Weinstein conjecture, we seek to find closed leaves for such contact foliations. By generalising ideas already employed successfully in proving the Weinstein conjecture in the past, we obtain the existence of closed leaves in particular cases when the foliation is either hyperbolic or C1-equicontinuous. This later class encompasses those of quasiconformal, conformal, isometric, and Riemannian contact foliations. Moreover, using techniques from Morse Theory, we were able to relate the closed leaves of a C1-equicontinuous contact foliation to its basic cohomology, obtaining a lower bound for the number of closed orbits, as a function of the foliations codimension.
  • DOI: 10.11606/T.55.2023.tde-30082023-163143
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação
  • Data de criação/publicação: 2023-03-10
  • Formato: Adobe PDF
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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