Jet isomorphism for conformal geometry
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 389-415 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi.
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi.
Classification : 53B20
Keywords: conformal geometry; ambient metric; jet isomorphism; deformation complex
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     author = {Graham, Robin C.},
     title = {Jet isomorphism for conformal geometry},
     journal = {Archivum mathematicum},
     pages = {389--415},
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     zbl = {1199.53044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a5/}
}
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Graham, Robin C. Jet isomorphism for conformal geometry. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 389-415. http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a5/

[1] Bailey T. N., Eastwood M. G., Graham C. R.: Invariant theory for conformal and CR geometry. Ann. of Math. (2) 139 (1994), 491–552. | MR | Zbl

[2] Branson T., Gover A. R.: Conformally invariant operators, differential forms, cohomology and a generalisation of Q-curvature. Comm. P.D.E. 30 (2005), 1611–1669, arXiv:math/0309085. | MR | Zbl

[3] Calderbank D. M. J., Diemer T.: Differential invariants and curved Bernstein-Gelfand-Gelfand sequences. J. Reine Angew. Math. 537 (2001), 67–103, arXiv:math/0001158. | MR | Zbl

[4] Čap A., Gover A. R.: Standard tractors and the conformal ambient metric construction. Ann. Global Anal. Geom. 24 (2003), 231–259, arXiv:math/0207016. | MR | Zbl

[5] Čap A., Slovák J., Souček V.: Bernstein-Gelfand-Gelfand sequences. Ann. of Math. (2) 154 (2001), 97–113. | MR

[6] Eastwood M. G., Graham C. R.: Invariants of conformal densities. Duke Math. J. 63 (1991), 633–671. | MR | Zbl

[7] Epstein D.: Natural tensors on Riemannian manifolds. J. Differential Geom. 10 (1975), 631–645. | MR | Zbl

[8] Fefferman C.,: Parabolic invariant theory in complex analysis. Adv. Math. 31 (1979), 131–262. | MR | Zbl

[9] Fefferman C., Graham C. R.: Conformal invariants. in The mathematical heritage of Élie Cartan (Lyon, 1984), Astérisque, 1985, Numero Hors Serie, 95–116. | MR

[10] Fefferman C., Graham C. R.: The ambient metric. arXiv:0710.0919.

[11] Gasqui J., Goldschmidt H.: Déformations Infinitésimales des Structures Conformes Plates. Prog. Math. 52, Birkhäuser, 1984. | MR | Zbl

[12] Gover A. R.: Invariant theory and calculus for conformal geometries. Adv. Math. 163 (2001), 206–257. | MR | Zbl

[13] Gover A. R., Peterson L. J.: The ambient obstruction tensor and the conformal deformation complex. Pacific J. Math. 226 (2006), 309–351, arXiv:math/0408229. | MR | Zbl

[14] Graham C. R., Hirachi K.: Inhomogeneous ambient metrics. IMA Vol. Math. Appl. 144: Symmetries and Overdetermined Systems of Partial Differential Equations, Springer, to appear, arXiv:math/0611931. | MR | Zbl

[15] Graham C. R., Hirachi K.: Ambient realization of conformal jets and deformation complex. in preparation.

[16] Hirachi K.: Construction of boundary invariants and the logarithmic singularity of the Bergman kernel. Ann. of Math. (2) 151 (2000), 151–191, arXiv:math/0010014. | MR

[17] Lepowsky J.: A generalization of the Bernstein-Gelfand-Gelfand resolution. J. Algebra 49 (1977), 496–511. | MR | Zbl