Conformally invariant differential operators and bilinear functionals in six dimensions

• Ugalde G, William J. ^[1]
  1. [1] Universidad de Costa Rica

     Universidad de Costa Rica

     Hospital, Costa Rica

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 15, Nº. 1, 2008, págs. 83-95
• Idioma: inglés
• DOI: 10.15517/rmta.v15i1.290
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Revisamos como construir el operador de Paneitz en cuatro dimensiones y el correspondienteoperador en seis dimensiones, mediante la construcci´on de funcionalesdiferenciales bilineales sim´etricos que son conformemente invariantes.Palabras clave: Invariantes conformes, operador de Paneitz, funcionales bilineales diferenciales.

  • English

    We review how to construct the Paneitz operator in dimension four and the correspondingoperator in dimension six, by constructing symmetric bilinear differentialfunctionals that are conformally invariant.Keywords: Conformal invariants, Paneitz operator, bilinear differential functionals.

• Referencias bibliográficas
  • Branson, T.P. (2001) “Automated symbolic computations in spin geometry”, in: F. Brackx, J.S.R. Chisholm & V. Souček (Eds.) Clifford Analysis...
  • Branson, T.P. (1985) “Differential operators canonically associated to a conformal structure”, Math. Scand. 57: 293–345.
  • Connes, A. (1995) “Quantized calculus and applications”, in: Proceedings of the XIth International Congress of Mathematical Physics, International...
  • Fefferman, C.; Graham, C.R. (1985) Conformal Invariants. In Élie Cartan et les mathématiques d’aujourd’hui , Astérisque, hors série, Société...
  • Graham, R.; Jenne, R.; Mason, L.; Sparling, G. (1992) “Conformally invariant powers of the Laplacian, I: Existence”, J. London Math. Soc....
  • Gover, A. R.; Peterson, L.J. (2003) “Conformally invariant powers of the Laplacian, Q-curvature and tractor calculus”, Comm. Math. Phys. 235(2):...
  • Lee, J.M. (s.f.) “A Mathematica package for doing tensor calculations in differential geometry”, available at http://www.math.washington.edu/∼lee/Ricci/.
  • Paneitz, S. (1983) “A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds”, preprint, Massachusetts...
  • Phillips, N.G.; Hu, B.L. (2003) “Noise kernel and stress energy bi-tensor of quantum fields in conformally-optical metrics: Schwarzschild...
  • Phillips, N.G.; Hu, B.L. (2001) “Noise kernel and stress energy bi-tensor of quantum fields in hot flat space and Gaussian approximation in...
  • Tsantalis, E.; Puntigam, R.A.; Hehl, F.W. (1996) “A quadratic curvature Lagrangian of Pawlowski and Raczka: a finger exercise with math tensor”,...
  • Ugalde, W.J. (2006) “A construction of critical GJMS operators using Wodzicki’s residue” Comm. Math. Phys. 261(3): 771–788.