Geometry of bifurcation sets of generic unfoldings of corank two functions

Detalhes bibliográficos
Autor(a) principal: Saji, Kentaro
Data de Publicação: 2021
Outros Autores: dos Santos, Samuel Paulino [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s00605-021-01607-8
http://hdl.handle.net/11449/229209
Resumo: We study the geometry of bifurcation sets of generic unfoldings of D4±-functions. Taking blow-ups, we show each of the bifurcation sets of D4±-functions admits a parametrization as a surface in R3. Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.
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spelling Geometry of bifurcation sets of generic unfoldings of corank two functionsBifurcation setCausticsParabolic curvePrincipal curvatureWe study the geometry of bifurcation sets of generic unfoldings of D4±-functions. Taking blow-ups, we show each of the bifurcation sets of D4±-functions admits a parametrization as a surface in R3. Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.Japan Society for the Promotion of ScienceFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Department of Mathematics Graduate School of Science Kobe University, Rokkodai 1-1, NadaDepartamento de Matemática Ibilce Universidade Estadual Paulista (Unesp), R. Cristóvão Colombo, 2265, Jd NazarethDepartamento de Matemática Ibilce Universidade Estadual Paulista (Unesp), R. Cristóvão Colombo, 2265, Jd NazarethJapan Society for the Promotion of Science: 18K03301FAPESP: 2019/10156-4Kobe UniversityUniversidade Estadual Paulista (UNESP)Saji, Kentarodos Santos, Samuel Paulino [UNESP]2022-04-29T08:31:15Z2022-04-29T08:31:15Z2021-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article553-575http://dx.doi.org/10.1007/s00605-021-01607-8Monatshefte fur Mathematik, v. 196, n. 3, p. 553-575, 2021.0026-9255http://hdl.handle.net/11449/22920910.1007/s00605-021-01607-82-s2.0-85111164596Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMonatshefte fur Mathematikinfo:eu-repo/semantics/openAccess2022-04-29T08:31:15Zoai:repositorio.unesp.br:11449/229209Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:37:55.765047Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Geometry of bifurcation sets of generic unfoldings of corank two functions
title Geometry of bifurcation sets of generic unfoldings of corank two functions
spellingShingle Geometry of bifurcation sets of generic unfoldings of corank two functions
Saji, Kentaro
Bifurcation set
Caustics
Parabolic curve
Principal curvature
title_short Geometry of bifurcation sets of generic unfoldings of corank two functions
title_full Geometry of bifurcation sets of generic unfoldings of corank two functions
title_fullStr Geometry of bifurcation sets of generic unfoldings of corank two functions
title_full_unstemmed Geometry of bifurcation sets of generic unfoldings of corank two functions
title_sort Geometry of bifurcation sets of generic unfoldings of corank two functions
author Saji, Kentaro
author_facet Saji, Kentaro
dos Santos, Samuel Paulino [UNESP]
author_role author
author2 dos Santos, Samuel Paulino [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Kobe University
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Saji, Kentaro
dos Santos, Samuel Paulino [UNESP]
dc.subject.por.fl_str_mv Bifurcation set
Caustics
Parabolic curve
Principal curvature
topic Bifurcation set
Caustics
Parabolic curve
Principal curvature
description We study the geometry of bifurcation sets of generic unfoldings of D4±-functions. Taking blow-ups, we show each of the bifurcation sets of D4±-functions admits a parametrization as a surface in R3. Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.
publishDate 2021
dc.date.none.fl_str_mv 2021-11-01
2022-04-29T08:31:15Z
2022-04-29T08:31:15Z
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://dx.doi.org/10.1007/s00605-021-01607-8
Monatshefte fur Mathematik, v. 196, n. 3, p. 553-575, 2021.
0026-9255
http://hdl.handle.net/11449/229209
10.1007/s00605-021-01607-8
2-s2.0-85111164596
url http://dx.doi.org/10.1007/s00605-021-01607-8
http://hdl.handle.net/11449/229209
identifier_str_mv Monatshefte fur Mathematik, v. 196, n. 3, p. 553-575, 2021.
0026-9255
10.1007/s00605-021-01607-8
2-s2.0-85111164596
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Monatshefte fur Mathematik
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 553-575
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128680878145536

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