Jet isomorphism for conformal geometry
Graham, Robin C.
Archivum Mathematicum, Tome 043 (2007), p. 389-415 / Harvested from 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.

Publié le : 2007-01-01
Classification:  53B20 
@article{108080,
     author = {Robin C. Graham},
     title = {Jet isomorphism for conformal geometry},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {389-415},
     zbl = {1199.53044},
     mrnumber = {2381784},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108080}
}

Graham, Robin C. Jet isomorphism for conformal geometry. Archivum Mathematicum, Tome 043 (2007) pp. 389-415. http://gdmltest.u-ga.fr/item/108080/

Bailey T. N.; Eastwood M. G.; Graham C. R. Invariant theory for conformal and CR geometry, Ann. of Math. (2) 139 (1994), 491–552. (1994) | MR 1283869 | Zbl 0814.53017

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 2182307 | Zbl 1226.58011

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 1856258 | Zbl 0985.58002

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 1996768 | Zbl 1039.53021

Čap A.; Slovák J.; Souček V. Bernstein-Gelfand-Gelfand sequences, Ann. of Math. (2) 154 (2001), 97–113. | MR 1847589

Eastwood M. G.; Graham C. R. Invariants of conformal densities, Duke Math. J. 63 (1991), 633–671. (1991) | MR 1121149 | Zbl 0745.53007

Epstein D. Natural tensors on Riemannian manifolds, J. Differential Geom. 10 (1975), 631–645. (1975) | MR 0415531 | Zbl 0321.53039

Fefferman C., Parabolic invariant theory in complex analysis, Adv. Math. 31 (1979), 131–262. (1979) | MR 0526424 | Zbl 0444.32013

Fefferman C.; Graham C. R. Conformal invariants, in The mathematical heritage of Élie Cartan (Lyon, 1984), Astérisque, 1985, Numero Hors Serie, 95–116. (1984) | MR 0837196

Fefferman C.; Graham C. R. The ambient metric, arXiv:0710.0919.

Gasqui J.; Goldschmidt H. Déformations Infinitésimales des Structures Conformes Plates, Prog. Math. 52, Birkhäuser, 1984. (1984) | MR 0776970 | Zbl 0585.53001

Gover A. R. Invariant theory and calculus for conformal geometries, Adv. Math. 163 (2001), 206–257. | MR 1864834 | Zbl 1004.53010

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 2247867 | Zbl 1125.53010

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 2384722 | Zbl 1148.53023

Graham C. R.; Hirachi K. Ambient realization of conformal jets and deformation complex, in preparation.

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. (191,) | MR 1745015

Lepowsky J. A generalization of the Bernstein-Gelfand-Gelfand resolution, J. Algebra 49 (1977), 496–511. (1977) | MR 0476813 | Zbl 0381.17006