The prescribed curvature problem in dimension four.
| dc.contributor.author | Muñoz Masqué, Jaime | |
| dc.contributor.author | Pozo Coronado, Luis Miguel | |
| dc.contributor.author | Sánchez Rodríguez, I. | |
| dc.date.accessioned | 2023-06-20T09:43:04Z | |
| dc.date.available | 2023-06-20T09:43:04Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | Necessary and sufficient conditions for a g-valued differential 2-form on a 4-dimensional manifold to be, locally, a curvature; form, are given. The dimension four is exceptional for the problem of prescribed curvature as, in this dimension, Bianchi's identities can be eliminated for a large class of Lie algebras, including semisimple algebras. Hence, the curvature forms are characterized as the solutions to a second-order partial differential system, which is proved to be formally integrable. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación | |
| dc.description.sponsorship | Junta de Andalucía, P.A.I. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17484 | |
| dc.identifier.doi | 10.1016/j.matpur.2009.10.003 | |
| dc.identifier.issn | 0021-7824 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0021782409001317 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50239 | |
| dc.journal.title | Journal de Mathématiques Pures et Appliquées | |
| dc.language.iso | eng | |
| dc.page.final | 612 | |
| dc.page.initial | 599 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2008-01386 | |
| dc.relation.projectID | FQM-324. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514 | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Bianchi identity | |
| dc.subject.keyword | Curvature form | |
| dc.subject.keyword | Formal integrability | |
| dc.subject.keyword | Lie algebra | |
| dc.subject.ucm | Geometría | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1204 Geometría | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | The prescribed curvature problem in dimension four. | |
| dc.type | journal article | |
| dc.volume.number | 92 | |
| dcterms.references | E. Angelopoulos, Algèbres de Lie g satisfaisant [g,g] = g, Derg = ad g, C. R. Acad. Sci. Paris Sér. I Math. 306 (13) (1988) 523–525. S. Benayadi, Structure of perfect Lie algebras without center and outer derivations, Ann. Fac. Sci. Toulouse Math. (6) 5 (2) (1996) 203–231. R.L. Bryant, S.S. Chern, R.B. Gardner, H.L. Goldschmidt, P.A. Griffiths, Exterior Differential Systems, Mathematical Sciences Research Institute Publications, vol. 18, Springer-Verlag, New York, 1991. D. DeTurck, H. Goldschmidt, J. Talvacchia, Connections with prescribed curvature and Yang–Mills currents: The semi-simple case, Ann. Sci.École Norm. Sup. (4) 24 (1) (1991) 57–112. D. DeTurck, H. Goldschmidt, J. Talvacchia, Local existence of connections with prescribed curvature, in: Differential Geometry, Global Analysis, and Topology, Halifax, NS, 1990, in: CMS Conf. Proc., vol. 12, Amer. Math. Soc., Providence, RI, 1991, pp. 13–25. V.V. Gorbatsevich, A.L. Onishchik, E.B. Vinberg, Lie Groups and Lie Algebras III. Structure of Lie Groups and Lie Algebras, Encyclopaedia Math. Sci., vol. 41, Springer-Verlag, Berlin, 1994;English transl. of: A.L. Onishchik, V.V. Gorbatsevich, E.B. Vinberg, Lie Groups and Lie Algebras III, in: Current Problems in Mathematics.Fundamental Directions, in: Itogi Nauki i Tekhniki, vol. 41, Akad. Nauk SSSR, Moscow, 1990. J.L. Koszul, Fibre Bundles and Differential Geometry, Tata Institute of Fundamental Research, Bombay, 1960. I.S. Krasil’shchik, V.V. Lychagin, A.M. Vinogradov,Geometry of jet spaces and nonlinear partial differential equations, in: A.B. Sosinskii (Ed.), Advanced Studies in Contemporary Mathematics, vol. 1, Gordon and Breach Science Publishers, New York, 1986 (translated from the Russian). M.A. Mostow, S. Shnider, Does a generic connection depend continuously on its curvature? Comm. Math. Phys. 90 (3) (1983) 417–432. M.A. Mostow, S. Shnider, Counterexamples to some results on the existence of field copies, Comm. Math. Phys. 90 (4)(1983) 521–526. M.A. Mostow, S. Shnider, The continuity of computing connections from curvatures, and of dividing smooth functions, in: Differential Geometric Methods in Mathematical Physics, Jerusalem, 1982, in: Math. Phys.Stud., vol. 6, Reidel, Dordrecht, 1984, pp. 45–54. S.P. Tsarev, Which 2-forms are locally curvature forms? Funktsional. Anal. i Prilozhen. 16 (3) (1982) 90–91 (in Russian); English transl.:Funct. Anal. Appl. 16 (3) (1982) 235–237. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0124d449-632e-4dc8-9651-eb1975f330ab | |
| relation.isAuthorOfPublication.latestForDiscovery | 0124d449-632e-4dc8-9651-eb1975f330ab |
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