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Conformal invariants and spherical contacts of surfaces in R^4

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Conformal invariants and spherical contacts of surfaces in R^4

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dc.contributor.author Romero-Fuster, M.C es_ES
dc.contributor.author Sanabria Codesal, Esther es_ES
dc.date.accessioned 2014-12-17T18:37:44Z
dc.date.available 2014-12-17T18:37:44Z
dc.date.issued 2013-01
dc.identifier.issn 1139-1138
dc.identifier.uri http://hdl.handle.net/10251/45567
dc.description.abstract Based on the fact that conformal maps preserve contacts of surfaces with hyperspheres, we introduce the concept of strong principal lines on surfaces in ℝ4 and obtain conformally invariant differential 1-forms along them. The zeros of these 1-forms are respectively characterized as ridges (singularities of squared-distance functions of type A k ,k≥4) and higher order semiumbilics (singularities of type D k ,k≥5). As a consequence we obtain that any closed orientable surface generically immersed in ℝ4 has at least 2 semiumbilic points of type D 5. We provide geometrical interpretations of these conformally invariant 1-forms in terms of the geometry of curves induced in the 5-dimensional de Sitter space and in the 5-dimensional lightcone. es_ES
dc.description.sponsorship Work of both authors partially supported by DGCYT-FEDER grant no. MTM2009-08933. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Revista Matemática Complutense es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Immersed surfaces es_ES
dc.subject Curvature ellipse es_ES
dc.subject Semiumbilics es_ES
dc.subject Ridges es_ES
dc.subject Conformal invariants es_ES
dc.subject De Sitter space es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Conformal invariants and spherical contacts of surfaces in R^4 es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s13163-011-0086-3
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2009-08933/ES/Singularidades, Geometria Generica Y Morfologia Matematica/ es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Romero-Fuster, M.; Sanabria Codesal, E. (2013). Conformal invariants and spherical contacts of surfaces in R^4. Revista Matemática Complutense. 26(1):215-240. https://doi.org/10.1007/s13163-011-0086-3 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://link.springer.com/article/10.1007%2Fs13163-011-0086-3 es_ES
dc.description.upvformatpinicio 215 es_ES
dc.description.upvformatpfin 240 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 26 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 235864
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
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