Chern-Gauss-Bonnet theorem for Grushin manifolds

Detalhes bibliográficos
Autor(a) principal: Lucas, Simão Andrade
Data de Publicação: 2023
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/41056
Resumo: The purpose of this dissertation is to provide a Chern-Gauss-Bonnet formula for Grushin manifolds. The theorem yields a geometric invariant linking asymptotically the geometry and topology of such manifolds to the geometry of the singular set. This invariant is obtained by asymptotically contracting a tubular neighborhood of the singular set. As consequences, the Chern-Gauss-Bonnet formula can be recovered, as well as a Gauss-Bonnet formula for two dimensional almost Riemannian structures.
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spelling Chern-Gauss-Bonnet theorem for Grushin manifoldsChern-Gauss-Bonnet theoremGrushin manifoldsManifolds with singularitiesThe purpose of this dissertation is to provide a Chern-Gauss-Bonnet formula for Grushin manifolds. The theorem yields a geometric invariant linking asymptotically the geometry and topology of such manifolds to the geometry of the singular set. This invariant is obtained by asymptotically contracting a tubular neighborhood of the singular set. As consequences, the Chern-Gauss-Bonnet formula can be recovered, as well as a Gauss-Bonnet formula for two dimensional almost Riemannian structures.O objectivo desta dissertação é apresentar uma fórmula de Chern-Gauss-Bonnet para as variedades de Grushin. O teorema concebe uma invariante geométrica que conecta assintoticamente a geometria e a topologia dessas variedades com a geometria do conjunto singular. Esta invariante é obtida contraindo assimptoticamente uma vizinhança tubular do conjunto singular. Como consequências, a fórmula de Chern-Gauss-Bonnet pode ser recuperada, bem como uma fórmula de Gauss-Bonnet para estruturas quase Riemannianas de duas dimensões.2024-03-13T09:55:18Z2023-07-11T00:00:00Z2023-07-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10773/41056engLucas, Simão Andradeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-18T01:48:28Zoai:ria.ua.pt:10773/41056Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T04:02:09.740557Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Chern-Gauss-Bonnet theorem for Grushin manifolds
title Chern-Gauss-Bonnet theorem for Grushin manifolds
spellingShingle Chern-Gauss-Bonnet theorem for Grushin manifolds
Lucas, Simão Andrade
Chern-Gauss-Bonnet theorem
Grushin manifolds
Manifolds with singularities
title_short Chern-Gauss-Bonnet theorem for Grushin manifolds
title_full Chern-Gauss-Bonnet theorem for Grushin manifolds
title_fullStr Chern-Gauss-Bonnet theorem for Grushin manifolds
title_full_unstemmed Chern-Gauss-Bonnet theorem for Grushin manifolds
title_sort Chern-Gauss-Bonnet theorem for Grushin manifolds
author Lucas, Simão Andrade
author_facet Lucas, Simão Andrade
author_role author
dc.contributor.author.fl_str_mv Lucas, Simão Andrade
dc.subject.por.fl_str_mv Chern-Gauss-Bonnet theorem
Grushin manifolds
Manifolds with singularities
topic Chern-Gauss-Bonnet theorem
Grushin manifolds
Manifolds with singularities
description The purpose of this dissertation is to provide a Chern-Gauss-Bonnet formula for Grushin manifolds. The theorem yields a geometric invariant linking asymptotically the geometry and topology of such manifolds to the geometry of the singular set. This invariant is obtained by asymptotically contracting a tubular neighborhood of the singular set. As consequences, the Chern-Gauss-Bonnet formula can be recovered, as well as a Gauss-Bonnet formula for two dimensional almost Riemannian structures.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-11T00:00:00Z
2023-07-11
2024-03-13T09:55:18Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/41056
url http://hdl.handle.net/10773/41056
dc.language.iso.fl_str_mv eng
language eng
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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