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Revista de Matemática Teoría y Aplicaciones
versão impressa ISSN 1409-2433
Rev. Mat vol.21 no.2 San José Jul./Dez. 2014
G -estructuras de orden superior
Superior order G –structures
Resumen
Estudiamos los rudimentos básicos sobre G-estructuras de orden superior, y luego probamos que el conjunto de automorfismos infinitesimales de una G-estructura geométrica sobre una variedad M es un grupo de Lie.
Palabras clave: haz fibrado principal; haz asociado; G-estructura.
Abstract
In this article we study the basic facts about superior order G-structures, then we show that the set of infinitesimally automorphisms of a geometric G-structure is a closed Lie group.
Keywords: principal fiber bundle; associated bundle; G-structure.
Mathematics Subject Classification: 53C05; 53C10.
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Referencias
[1] Candel, A.; Quiroga-Barranco, R. (2004) “Rigid and finite type geometric structures”, Geometriae Dedicata 106: 123–143. [ Links ]
[2] D’Ambra, G.; Gromov, M. (1991) “Lectures in transformation groups: geometry and dynamics”, Surveys in Differential Geometry 1: 19–111. [ Links ]
[3] Duistermaat, J.J.; Kolk, J.A.C (2000) Lie Groups. Universitext, Springer-Verlag, Berlin. [ Links ]
[4] Feres, R. (1998) Dynamical Systems and Semisimple Groups. An Introduction. Tracts in Mathematics 126, CambridgeUniversity Press, New York. [ Links ]
[5] Gromov, M. (1988) Rigid transformations groups, in: D. Bernard & Y. Choquet-Bruhat (Eds.) Géométrie Différentielle, Travaux en Cours, Hermann, Paris: 65–139. [ Links ]
[6] Kobayashi, S.; Nomizu, K. (1980) Foundations of Differential Geometry, Vol. 1, John Wiley & Sons, New York. [ Links ]
[7] Kolá?r, I.; Michor, P.W.; Slovák, J. (1993) Natural Operations in Differential Geometry, Springer-Verlag, Berlin. [ Links ]
[8] Rosales, J. (2005) The Gromov’s Centralizer Theorem for Semisimple Lie group Actions. Ph.D Thesis, Centro de Investigación y EstudiosAvanzados del Instituto Politécnico Nacional, México. [ Links ]
[2] D’Ambra, G.; Gromov, M. (1991) “Lectures in transformation groups: geometry and dynamics”, Surveys in Differential Geometry 1: 19–111. [ Links ]
[3] Duistermaat, J.J.; Kolk, J.A.C (2000) Lie Groups. Universitext, Springer-Verlag, Berlin. [ Links ]
[4] Feres, R. (1998) Dynamical Systems and Semisimple Groups. An Introduction. Tracts in Mathematics 126, CambridgeUniversity Press, New York. [ Links ]
[5] Gromov, M. (1988) Rigid transformations groups, in: D. Bernard & Y. Choquet-Bruhat (Eds.) Géométrie Différentielle, Travaux en Cours, Hermann, Paris: 65–139. [ Links ]
[6] Kobayashi, S.; Nomizu, K. (1980) Foundations of Differential Geometry, Vol. 1, John Wiley & Sons, New York. [ Links ]
[7] Kolá?r, I.; Michor, P.W.; Slovák, J. (1993) Natural Operations in Differential Geometry, Springer-Verlag, Berlin. [ Links ]
[8] Rosales, J. (2005) The Gromov’s Centralizer Theorem for Semisimple Lie group Actions. Ph.D Thesis, Centro de Investigación y EstudiosAvanzados del Instituto Politécnico Nacional, México. [ Links ]
* School of Mathematics, Instituto Tecnológico de Costa Rica y Universidad de Costa Rica, Costa Rica. E-Mail: jose.rosales@ucr.ac.cr
Received: 18/Mar/2011; Revised: 17/Dec/2013; Accepted: 15/Jan/2014
