Mostrar el registro sencillo del ítem
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 |
dc.description.references | Arnol’d, V.I., Gusein-Zade, S.M., Varchenko, A.N.: Singularities of Differentiable Maps. Monographs in Mathematics, vol. 82. Birkhäuser, Boston (1985) | es_ES |
dc.description.references | Beardon, A.F.: The Geometry of Discrete Groups. Springer, Berlin (1983) | es_ES |
dc.description.references | Coxeter, H.S.M.: Inversive distance. Ann. Mat. Pura Appl. 4(71), 73–83 (1966) | es_ES |
dc.description.references | Deheuvels, R.: Groupes conformes et algèbres de Clifford. Rend. Semin. Mat. (Torino) 43(2), 205–226 (1985) | es_ES |
dc.description.references | Golubitsky, M., Gillemin, V.: Stable Mappings and Their Singularities. Springer, Berlin (1973) | es_ES |
dc.description.references | Langevin, R.J., O’Hara, J.: Conformal arc-length as $\frac{1}{2}$ -dimensional length of the set of osculating circles. Comment. Math. Helv. 85, 273–312 (2010) | es_ES |
dc.description.references | Little, J.: On singularites of submanifolds of higher dimensional Euclidean space. Ann. Mat. Pura Appl., Ser. 4A 83, 261–336 (1969) | es_ES |
dc.description.references | Looijenga, E.J.N.: Structural stability of smooth families of C ∞-functions. Doctoral Thesis, University of Amsterdam (1974) | es_ES |
dc.description.references | Mochida, D.K.H., Romero-Fuster, M.C., Ruas, M.A.S.: The geometry of surfaces in 4-space from a contact viewpoint. Geom. Dedic. 54, 323–333 (1995) | es_ES |
dc.description.references | Monera, M.G., Montesinos Amilibia, A., Sanabria Codesal, E.: The Taylor expansion of the exponential map and geometric applications. Preprint | es_ES |
dc.description.references | Montaldi, J.A.: Contact with application to submanifolds. Ph.D. Thesis, University of Liverpool (1983) | es_ES |
dc.description.references | Montaldi, J.A.: On generic composites of maps. Bull. Lond. Math. Soc. 23, 81–85 (1991) | es_ES |
dc.description.references | Montesinos Amilibia, A., Romero Fuster, M.C., Sanabria Codesal, E.: Conformal curvatures of curves in ℝ n+1. Indag. Math. 12(3), 369–382 (2001) | es_ES |
dc.description.references | Moraes, S., Romero Fuster, M.C.: Semiumbilics and normal fields on surfaces immersed in ℝ n ,n>3. Rocky Mt. J. Math. 35(4), 1327–1346 (2005) | es_ES |
dc.description.references | Porteous, I.R.: The normal singularities of a submanifold. J. Differ. Geom. 5, 543–564 (1971) | es_ES |
dc.description.references | Porteous, I.R.: Geometric Differentiation for the Intelligence of Curves and Surfaces. Cambridge University Press, Cambridge (2001) | es_ES |
dc.description.references | Romero-Fuster, M.C.: Stereographic projections and geometric singularities. In: Workshop on Real and Complex Singularities, São Carlos, 1996. Mat. Contemp., vol. 12, pp. 167–182 (1997) | es_ES |
dc.description.references | Romero-Fuster, M.C., Sanabria-Codesal, E.: Generalized evolutes, vertices and conformal invariants of curves in ℝ n+1. Indag. Math. 10(2), 297–305 (1999) | es_ES |
dc.description.references | Romero-Fuster, M.C., Sanabria-Codesal, E.: Lines of curvature, ridges and conformal invariants of hypersurfaces. Beitrage Algebra Geom. 45(2), 615–635 (2004) | es_ES |
dc.description.references | Romero-Fuster, M.C., Sanchéz-Bringas, F.: Umbilicity of surfaces with orthogonal asymptotic lines in ℝ4. Differ. Geom. Appl. 16, 213–224 (2002) | es_ES |
dc.description.references | Romero-Fuster, M.C., Ruas, M.A.S., Tari, F.: Asymptotic curves on surfaces in ℝ5. Commun. Contemp. Math. 10, 309–335 (2008) | es_ES |