Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-4-431-56021-0_14 http://hdl.handle.net/11449/173179 |
Resumo: | We define cuspidal curvature Kc (resp. normalized cuspidal curvature μc) along cuspidal edges (resp. at a swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product KΠ called the product curvature (resp. μΠ called normalized product curvature) of Kc (resp. μc) and the limiting normal curvature Kv is an intrinsic invariant of the surface, and is closely related to the boundedness of the Gaussian curvature. We also consider the limiting behavior of KΠ when cuspidal edges accumulate to other singularities. Moreover, several new geometric invariants of cuspidal edges and swallowtails are given. |
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Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave frontsCuspidal cross capCuspidal edgeGaussian curvatureMean curvatureSingularitiesSwallowtailWave frontWe define cuspidal curvature Kc (resp. normalized cuspidal curvature μc) along cuspidal edges (resp. at a swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product KΠ called the product curvature (resp. μΠ called normalized product curvature) of Kc (resp. μc) and the limiting normal curvature Kv is an intrinsic invariant of the surface, and is closely related to the boundedness of the Gaussian curvature. We also consider the limiting behavior of KΠ when cuspidal edges accumulate to other singularities. Moreover, several new geometric invariants of cuspidal edges and swallowtails are given.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Japan Society for the Promotion of ScienceDepartamento de Matemática IBILCE—UNESP R. Cristovao Colombo, 2265, CEP, Sao Jose do Rio PretoDepartment of Mathematics Faculty of Science Kobe University, RokkoDepartment of Mathematical and Computing Sciences Tokyo Institute of TechnologyDepartment of Mathematics Tokyo Institute of TechnologyDepartamento de Matemática IBILCE—UNESP R. Cristovao Colombo, 2265, CEP, Sao Jose do Rio PretoCAPES: BEX 12998/12-5Japan Society for the Promotion of Science: BEX 12998/12-5Universidade Estadual Paulista (Unesp)Kobe UniversityTokyo Institute of TechnologyMartins, L. F. [UNESP]Saji, K.Umehara, M.Yamada, K.2018-12-11T17:04:00Z2018-12-11T17:04:00Z2016-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject247-281http://dx.doi.org/10.1007/978-4-431-56021-0_14Springer Proceedings in Mathematics and Statistics, v. 154, p. 247-281.2194-10172194-1009http://hdl.handle.net/11449/17317910.1007/978-4-431-56021-0_142-s2.0-84977519375Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSpringer Proceedings in Mathematics and Statistics0,226info:eu-repo/semantics/openAccess2021-10-23T21:44:27Zoai:repositorio.unesp.br:11449/173179Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:05:45.374965Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
title |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
spellingShingle |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts Martins, L. F. [UNESP] Cuspidal cross cap Cuspidal edge Gaussian curvature Mean curvature Singularities Swallowtail Wave front |
title_short |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
title_full |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
title_fullStr |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
title_full_unstemmed |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
title_sort |
Behavior of gaussian curvature and mean curvature near non-degenerate singular points on wave fronts |
author |
Martins, L. F. [UNESP] |
author_facet |
Martins, L. F. [UNESP] Saji, K. Umehara, M. Yamada, K. |
author_role |
author |
author2 |
Saji, K. Umehara, M. Yamada, K. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Kobe University Tokyo Institute of Technology |
dc.contributor.author.fl_str_mv |
Martins, L. F. [UNESP] Saji, K. Umehara, M. Yamada, K. |
dc.subject.por.fl_str_mv |
Cuspidal cross cap Cuspidal edge Gaussian curvature Mean curvature Singularities Swallowtail Wave front |
topic |
Cuspidal cross cap Cuspidal edge Gaussian curvature Mean curvature Singularities Swallowtail Wave front |
description |
We define cuspidal curvature Kc (resp. normalized cuspidal curvature μc) along cuspidal edges (resp. at a swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product KΠ called the product curvature (resp. μΠ called normalized product curvature) of Kc (resp. μc) and the limiting normal curvature Kv is an intrinsic invariant of the surface, and is closely related to the boundedness of the Gaussian curvature. We also consider the limiting behavior of KΠ when cuspidal edges accumulate to other singularities. Moreover, several new geometric invariants of cuspidal edges and swallowtails are given. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-01-01 2018-12-11T17:04:00Z 2018-12-11T17:04:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-4-431-56021-0_14 Springer Proceedings in Mathematics and Statistics, v. 154, p. 247-281. 2194-1017 2194-1009 http://hdl.handle.net/11449/173179 10.1007/978-4-431-56021-0_14 2-s2.0-84977519375 |
url |
http://dx.doi.org/10.1007/978-4-431-56021-0_14 http://hdl.handle.net/11449/173179 |
identifier_str_mv |
Springer Proceedings in Mathematics and Statistics, v. 154, p. 247-281. 2194-1017 2194-1009 10.1007/978-4-431-56021-0_14 2-s2.0-84977519375 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Springer Proceedings in Mathematics and Statistics 0,226 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
247-281 |
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 |
|
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1808128459305648128 |