Natural SU(2)-structures on tangent sphere bundles

Detalhes bibliográficos
Autor(a) principal: Albuquerque, Rui
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/30972
https://doi.org/Albuquerque, R., Natural SU(2)-structures on tangent sphere bundles, Asian Journal of Mathematics, Vol 24, 3 (2020), pp. 457-482, https://dx.doi.org/10.4310/AJM.2020.v24.n3.a4
https://doi.org/10.4310/AJM.2020.v24.n3.a4
Resumo: We define and study natural SU(2)-structures, in the sense of Conti–Salamon, on the total space S of the tangent sphere bundle of any given oriented Riemannian 3-manifold M. We recur to a fundamental exterior differential system of Riemannian geometry. Essentially, two types of structures arise: the contact-hypo and the non-contact and, for each, we study the conditions for being hypo, nearly-hypo or double-hypo. We discover new double-hypo structures on S^3×S^2, of which the well-known Sasaki–Einstein are a particular case. Hyperbolic geometry examples also appear. In the search of the associated metrics, we find a theorem, useful for explicitly determining the metric, which applies to all SU(2)-structures in general. Within our application to tangent sphere bundles, we discover a whole new class of metrics specific to 3d-geometry. The evolution equations of Conti–Salamon are considered, leading us to a new integrable SU(3)-structure on S×ℝ^+ associated to any flat M.
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spelling Natural SU(2)-structures on tangent sphere bundlestangent bundleSU(n)-structurehypo structureevolution equationsWe define and study natural SU(2)-structures, in the sense of Conti–Salamon, on the total space S of the tangent sphere bundle of any given oriented Riemannian 3-manifold M. We recur to a fundamental exterior differential system of Riemannian geometry. Essentially, two types of structures arise: the contact-hypo and the non-contact and, for each, we study the conditions for being hypo, nearly-hypo or double-hypo. We discover new double-hypo structures on S^3×S^2, of which the well-known Sasaki–Einstein are a particular case. Hyperbolic geometry examples also appear. In the search of the associated metrics, we find a theorem, useful for explicitly determining the metric, which applies to all SU(2)-structures in general. Within our application to tangent sphere bundles, we discover a whole new class of metrics specific to 3d-geometry. The evolution equations of Conti–Salamon are considered, leading us to a new integrable SU(3)-structure on S×ℝ^+ associated to any flat M.International Press2022-01-31T15:41:58Z2022-01-312020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/30972https://doi.org/Albuquerque, R., Natural SU(2)-structures on tangent sphere bundles, Asian Journal of Mathematics, Vol 24, 3 (2020), pp. 457-482, https://dx.doi.org/10.4310/AJM.2020.v24.n3.a4http://hdl.handle.net/10174/30972https://doi.org/10.4310/AJM.2020.v24.n3.a4porhttps://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2020/0024/0003/AJM-2020-0024-0003-a004.pdfrpa_da@sapo.pt337Albuquerque, Ruiinfo: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:RCAAP2024-01-03T19:28:48Zoai:dspace.uevora.pt:10174/30972Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:20:02.132531Repositório 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 Natural SU(2)-structures on tangent sphere bundles
title Natural SU(2)-structures on tangent sphere bundles
spellingShingle Natural SU(2)-structures on tangent sphere bundles
Albuquerque, Rui
tangent bundle
SU(n)-structure
hypo structure
evolution equations
title_short Natural SU(2)-structures on tangent sphere bundles
title_full Natural SU(2)-structures on tangent sphere bundles
title_fullStr Natural SU(2)-structures on tangent sphere bundles
title_full_unstemmed Natural SU(2)-structures on tangent sphere bundles
title_sort Natural SU(2)-structures on tangent sphere bundles
author Albuquerque, Rui
author_facet Albuquerque, Rui
author_role author
dc.contributor.author.fl_str_mv Albuquerque, Rui
dc.subject.por.fl_str_mv tangent bundle
SU(n)-structure
hypo structure
evolution equations
topic tangent bundle
SU(n)-structure
hypo structure
evolution equations
description We define and study natural SU(2)-structures, in the sense of Conti–Salamon, on the total space S of the tangent sphere bundle of any given oriented Riemannian 3-manifold M. We recur to a fundamental exterior differential system of Riemannian geometry. Essentially, two types of structures arise: the contact-hypo and the non-contact and, for each, we study the conditions for being hypo, nearly-hypo or double-hypo. We discover new double-hypo structures on S^3×S^2, of which the well-known Sasaki–Einstein are a particular case. Hyperbolic geometry examples also appear. In the search of the associated metrics, we find a theorem, useful for explicitly determining the metric, which applies to all SU(2)-structures in general. Within our application to tangent sphere bundles, we discover a whole new class of metrics specific to 3d-geometry. The evolution equations of Conti–Salamon are considered, leading us to a new integrable SU(3)-structure on S×ℝ^+ associated to any flat M.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01T00:00:00Z
2022-01-31T15:41:58Z
2022-01-31
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/10174/30972
https://doi.org/Albuquerque, R., Natural SU(2)-structures on tangent sphere bundles, Asian Journal of Mathematics, Vol 24, 3 (2020), pp. 457-482, https://dx.doi.org/10.4310/AJM.2020.v24.n3.a4
http://hdl.handle.net/10174/30972
https://doi.org/10.4310/AJM.2020.v24.n3.a4
url http://hdl.handle.net/10174/30972
https://doi.org/Albuquerque, R., Natural SU(2)-structures on tangent sphere bundles, Asian Journal of Mathematics, Vol 24, 3 (2020), pp. 457-482, https://dx.doi.org/10.4310/AJM.2020.v24.n3.a4
https://doi.org/10.4310/AJM.2020.v24.n3.a4
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2020/0024/0003/AJM-2020-0024-0003-a004.pdf
rpa_da@sapo.pt
337
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv International Press
publisher.none.fl_str_mv International Press
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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