A fundamental differential system of 3-dimensional Riemannian geometry

Detalhes bibliográficos
Autor(a) principal: Albuquerque, Rui
Data de Publicação: 2018
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10174/24574
https://doi.org/10.1016/j.bulsci.2018.01.001
Resumo: We briefly recall a fundamental exterior differential system of Riemannian geometry and apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemannian 3-manifolds. In particular, we develop the study of ∇Ric. The exterior differential system leads to a remarkable Weingarten type equation for immersed surfaces in hyperbolic 3-space. A new independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system.
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spelling A fundamental differential system of 3-dimensional Riemannian geometrydifferential systemRiemannian manifold3-manifoldsWe briefly recall a fundamental exterior differential system of Riemannian geometry and apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemannian 3-manifolds. In particular, we develop the study of ∇Ric. The exterior differential system leads to a remarkable Weingarten type equation for immersed surfaces in hyperbolic 3-space. A new independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system.Elsevier2019-02-12T12:33:55Z2019-02-122018-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/24574https://doi.org/10.1016/j.bulsci.2018.01.001http://hdl.handle.net/10174/24574https://doi.org/10.1016/j.bulsci.2018.01.001engR. Albuquerque, A fundamental differential system of 3-dimensional Riemannian geometry, Bull. Sci. math. 143 (2018) 82-107.http://arxiv.org/abs/1112.3213rpa@uevora.pt337Albuquerque, Ruiinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-01-03T19:17:25Zoai:dspace.uevora.pt:10174/24574Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T12:17:34.817330Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv A fundamental differential system of 3-dimensional Riemannian geometry
title A fundamental differential system of 3-dimensional Riemannian geometry
spellingShingle A fundamental differential system of 3-dimensional Riemannian geometry
Albuquerque, Rui
differential system
Riemannian manifold
3-manifolds
title_short A fundamental differential system of 3-dimensional Riemannian geometry
title_full A fundamental differential system of 3-dimensional Riemannian geometry
title_fullStr A fundamental differential system of 3-dimensional Riemannian geometry
title_full_unstemmed A fundamental differential system of 3-dimensional Riemannian geometry
title_sort A fundamental differential system of 3-dimensional Riemannian geometry
author Albuquerque, Rui
author_facet Albuquerque, Rui
author_role author
dc.contributor.author.fl_str_mv Albuquerque, Rui
dc.subject.por.fl_str_mv differential system
Riemannian manifold
3-manifolds
topic differential system
Riemannian manifold
3-manifolds
description We briefly recall a fundamental exterior differential system of Riemannian geometry and apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemannian 3-manifolds. In particular, we develop the study of ∇Ric. The exterior differential system leads to a remarkable Weingarten type equation for immersed surfaces in hyperbolic 3-space. A new independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system.
publishDate 2018
dc.date.none.fl_str_mv 2018-03-01T00:00:00Z
2019-02-12T12:33:55Z
2019-02-12
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10174/24574
https://doi.org/10.1016/j.bulsci.2018.01.001
http://hdl.handle.net/10174/24574
https://doi.org/10.1016/j.bulsci.2018.01.001
url http://hdl.handle.net/10174/24574
https://doi.org/10.1016/j.bulsci.2018.01.001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv R. Albuquerque, A fundamental differential system of 3-dimensional Riemannian geometry, Bull. Sci. math. 143 (2018) 82-107.
http://arxiv.org/abs/1112.3213
rpa@uevora.pt
337
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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