Polynomial Weingarten surfaces of tubular type

Detalhes bibliográficos
Autor(a) principal: Silva, Fernando Gasparotto da
Data de Publicação: 2022
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFSCAR
Texto Completo: https://repositorio.ufscar.br/handle/ufscar/16052
Resumo: This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, Lorentzian and Hyperbolic spaces) that verify an arbitrary polynomial relation among its Gaussian and mean curvatures. The results obtained provide geometric features of the surface as well as algebraic conditions over the polynomial that defines a surface as Weingarten. Furthermore, results that allow us to investigate Weingarten surfaces only by the polynomial analysis are presented.
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spelling Silva, Fernando Gasparotto daBarreto, Alexandre Paivahttp://lattes.cnpq.br/3369766702725474http://lattes.cnpq.br/3794617946389521343595dc-aded-4ec8-bdae-236195e5085a2022-05-06T13:28:28Z2022-05-06T13:28:28Z2022-04-04SILVA, Fernando Gasparotto da. Polynomial Weingarten surfaces of tubular type. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16052.https://repositorio.ufscar.br/handle/ufscar/16052This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, Lorentzian and Hyperbolic spaces) that verify an arbitrary polynomial relation among its Gaussian and mean curvatures. The results obtained provide geometric features of the surface as well as algebraic conditions over the polynomial that defines a surface as Weingarten. Furthermore, results that allow us to investigate Weingarten surfaces only by the polynomial analysis are presented.Esse trabalho busca contribuir com a classificação de superfícies de Weingarten. Mais precisamente, esse trabalho classifica três famílias de superfícies (a saber, as superfícies: tubular, cíclica e canal) em um espaço tridimensional com curvatura seccional constante (os espaços Euclidiano, Lorentziano e Hiperbólico) que verificam uma relação arbitrária polinomial entre suas curvaturas Gaussiana e média. Os resultados obtidos fornecem características geométricas da superfície bem como condições algébricas sobre o polinômio que a define como superfície de Weingarten. Além disso, são apresentados resultados que nos permitem investigar superfícies de Weingarten exclusivamente através da análise polinomial.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)88882.426771/2019-01engUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessWeingarten surfacesWeingarten tubular surfacesWeingarten cyclic surfacesWeingarten canal surfacesPolynomial Weingarten surfaceSuperfície de WeingartenSuperfície tubular de WeingartenSuperfície cíclica de WeingartenSuperfície canal de WeingartenSuperfície polinomial de WeingartenCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIALPolynomial Weingarten surfaces of tubular typeSuperfícies de Weingarten polinomial do tipo tubularinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6006008f21d7f0-8ea2-44e6-9fc1-4fdc319c18acreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdfPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdfThesis: Polynomial Weingarten Surfaces of Tubular Type - Gasparotto da Silva, Fernando.application/pdf791845https://repositorio.ufscar.br/bitstream/ufscar/16052/1/Polynomial%20Weingarten%20Surfaces%20of%20Tubular%20Type%20-%20Gasparotto%20Silva%2c%20F..pdf05f4535eb568da961fd54524ff4749edMD51Carta Comprovante - Ass Barreto, A P.pdfCarta Comprovante - Ass Barreto, A P.pdfCarta Comprovante assinada por Barreto, A.P.application/pdf203469https://repositorio.ufscar.br/bitstream/ufscar/16052/3/Carta%20Comprovante%20-%20Ass%20Barreto%2c%20A%20P.pdfc1ecb3f33c3338f2073d2624280400f3MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/16052/4/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD54TEXTPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdf.txtPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdf.txtExtracted texttext/plain265382https://repositorio.ufscar.br/bitstream/ufscar/16052/5/Polynomial%20Weingarten%20Surfaces%20of%20Tubular%20Type%20-%20Gasparotto%20Silva%2c%20F..pdf.txt61e38b11fb30e6c9e8572ea06630299dMD55Carta Comprovante - Ass Barreto, A P.pdf.txtCarta Comprovante - Ass Barreto, A P.pdf.txtExtracted texttext/plain1359https://repositorio.ufscar.br/bitstream/ufscar/16052/7/Carta%20Comprovante%20-%20Ass%20Barreto%2c%20A%20P.pdf.txtf37e10b2afbfcd145a84a3189f20a988MD57THUMBNAILPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdf.jpgPolynomial Weingarten Surfaces of Tubular Type - Gasparotto Silva, F..pdf.jpgIM Thumbnailimage/jpeg6044https://repositorio.ufscar.br/bitstream/ufscar/16052/6/Polynomial%20Weingarten%20Surfaces%20of%20Tubular%20Type%20-%20Gasparotto%20Silva%2c%20F..pdf.jpg2b198bb5bf85ab6ba35484c11ae8000eMD56Carta Comprovante - Ass Barreto, A P.pdf.jpgCarta Comprovante - Ass Barreto, A P.pdf.jpgIM Thumbnailimage/jpeg6155https://repositorio.ufscar.br/bitstream/ufscar/16052/8/Carta%20Comprovante%20-%20Ass%20Barreto%2c%20A%20P.pdf.jpg0acfc6b446b1f7930d84f7f03479b06cMD58ufscar/160522023-09-18 18:32:25.41oai:repositorio.ufscar.br:ufscar/16052Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:25Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.eng.fl_str_mv Polynomial Weingarten surfaces of tubular type
dc.title.alternative.por.fl_str_mv Superfícies de Weingarten polinomial do tipo tubular
title Polynomial Weingarten surfaces of tubular type
spellingShingle Polynomial Weingarten surfaces of tubular type
Silva, Fernando Gasparotto da
Weingarten surfaces
Weingarten tubular surfaces
Weingarten cyclic surfaces
Weingarten canal surfaces
Polynomial Weingarten surface
Superfície de Weingarten
Superfície tubular de Weingarten
Superfície cíclica de Weingarten
Superfície canal de Weingarten
Superfície polinomial de Weingarten
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL
title_short Polynomial Weingarten surfaces of tubular type
title_full Polynomial Weingarten surfaces of tubular type
title_fullStr Polynomial Weingarten surfaces of tubular type
title_full_unstemmed Polynomial Weingarten surfaces of tubular type
title_sort Polynomial Weingarten surfaces of tubular type
author Silva, Fernando Gasparotto da
author_facet Silva, Fernando Gasparotto da
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/3794617946389521
dc.contributor.author.fl_str_mv Silva, Fernando Gasparotto da
dc.contributor.advisor1.fl_str_mv Barreto, Alexandre Paiva
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3369766702725474
dc.contributor.authorID.fl_str_mv 343595dc-aded-4ec8-bdae-236195e5085a
contributor_str_mv Barreto, Alexandre Paiva
dc.subject.eng.fl_str_mv Weingarten surfaces
Weingarten tubular surfaces
Weingarten cyclic surfaces
Weingarten canal surfaces
Polynomial Weingarten surface
topic Weingarten surfaces
Weingarten tubular surfaces
Weingarten cyclic surfaces
Weingarten canal surfaces
Polynomial Weingarten surface
Superfície de Weingarten
Superfície tubular de Weingarten
Superfície cíclica de Weingarten
Superfície canal de Weingarten
Superfície polinomial de Weingarten
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL
dc.subject.por.fl_str_mv Superfície de Weingarten
Superfície tubular de Weingarten
Superfície cíclica de Weingarten
Superfície canal de Weingarten
Superfície polinomial de Weingarten
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL
description This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, Lorentzian and Hyperbolic spaces) that verify an arbitrary polynomial relation among its Gaussian and mean curvatures. The results obtained provide geometric features of the surface as well as algebraic conditions over the polynomial that defines a surface as Weingarten. Furthermore, results that allow us to investigate Weingarten surfaces only by the polynomial analysis are presented.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-05-06T13:28:28Z
dc.date.available.fl_str_mv 2022-05-06T13:28:28Z
dc.date.issued.fl_str_mv 2022-04-04
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv SILVA, Fernando Gasparotto da. Polynomial Weingarten surfaces of tubular type. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16052.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/16052
identifier_str_mv SILVA, Fernando Gasparotto da. Polynomial Weingarten surfaces of tubular type. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16052.
url https://repositorio.ufscar.br/handle/ufscar/16052
dc.language.iso.fl_str_mv eng
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática - PPGM
dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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