Laplacian operators and Q-curvature on conformally Einstein manifolds

Mathematische Annalen

Volumn 336, Issue 2, 2006, Pages 311-334

  Gover, A R ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748864600     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-006-0004-z     Document Type: Article

References (33)

1. Bailey, T.N., Eastwood, M.G., Gover, A.R.: Thomas's structure bundle for conformal, projective and related structures. Rocky Mountain J. Math. 24, 1191-1217 (1994)
2. Branson, T.: Differential operators canonically associated to a conformal structure. Math. Scand. 57, 293-345 (1985)
3. Branson, T.: Sharp inequalities, the functional determinant, and the complementary series. Trans. Amer. Math. Soc. 347, 3671-3742 (1995)
4. Branson, T., Gover, A.R.: Conformally invariant operators, differential forms, cohomology and a generalisation of Q-curvature. Comm. Partial Differential Equations 30, 1611-1669 (2005)
5. Branson, T., Ørsted, B.: Explicit functional determinants in four dimensions. Proc. Amer. Math. Soc. 113, 669-682 (1991)
6. Brinkmann, H.W.: Einstein spaces which are mapped conformally on each other. Math. Ann. 94, 119-145 (1925)
7. Cartan, E.: Les espaces à connexion conforme. Ann. Soc. Pol. Math. 2, 171-202 (1923)
8. Čap, A., Gover, A.R.: Tractor bundles for irreducible parabolic geometries. In: Global analysis and harmonic analysis (Marseille-Luminy, 1999), pp. 129-154. Sémin. Congr., vol. 4, Soc. Math. France, Paris (2000)
9. Čap, A., Gover, A.R.: Tractor calculi for parabolic geometries. Trans. Amer. Math. Soc. 354, 1511-1548(2002)
10. Čap, A., Gover, A.R.: Standard tractors and the conformal ambient metric construction. Ann. Global Anal. Geom. 24(3), 231-259 (2003)
11. Chang, S.-Y. A., Gursky, M., Yang, P.: An equation of Monge-Ampere type in conformal geometry, and four manifolds of positive Ricci curvature. Ann. Math. 155, 709-787 (2002)
12. 4. Duke Math. J. 103, 523-544 (2000)
13. Djadli, Z., Malchiodi, A.: Existence of conformal metrics with constant Q-curvature. Preprint math.AP/0410141, http://www.arxiv.org
14. Dirac, P.A.M.: Wave equations in conformal space. Ann. Math. 37, 429-442 (1936)
15. Eastwood, M.G.: Notes on conformal differential geometry. In: The Proceedings of the 15th Winter School "Geometry and Physics" (Srni, 1995). Rend. Circ. Mat. Palermo (2) Suppl. No. 43 pp. 57-76 (1996)
16. Eastwood, M.G., Rice, J.W.: Conformally invariant differential operators on Minkowski space and their curved analogues. Comm. Math. Phys. 109, 207-228 (1987). Erratum, Comm. Math. Phys. 144, 213 (1992).
17. Eastwood, M.G., Slovák, J.: Semiholonomic Verma modules. J. Algebra 197, 424-448 (1997)
18. Fefferman, C., Graham, C.R.: Conformal invariants. The mathematical heritage of Élie Cartan (Lyon, 1984). Astérisque 1985, Numero Hors Série, pp. 95-116
19. Fefferman, C., Hirachi, K.: Ambient metric construction of Q-curvature in conformal and CR geometries. Math. Res. Lett. 10, 819-832 (2003)
20. Gauduchon, P.: Connexion canonique et structures de Weyl en geometrie conforme. Report: CNRS UA766 (1990)
21. Gover, A.R., Hirachi, K.: Conformally invariant powers of the Laplacian - A complete non-existence theorem. J. Amer. Math. Soc. 17, 389-405 (2004)
22. Gover, A.R., Nurowski, P.: Obstructions to conformally Einstein metrics in n dimensions. J. Geom. Phys. 56, 450-484 (2006)
23. Gover, A.R., Peterson, L.J.: Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus. Commun. Math. Phys. 235, 339-378 (2003)
24. Gover, A.R., Peterson, L.J.: The ambient obstruction tensor and the conformal deformation complex. Pacific J. Math., (in Press). math.DG/0408229, http://arXiv.org
25. Gover, A.R.: Aspects of parabolic invariant theory. In: The 18th Winter School "Geometry and Physics" (Srní 1998), pp. 25-47. Rend. Circ. Mat. Palermo (2) Suppl. No. 59 (1999)
26. Gover, A.R.: Invariant theory and calculus for conformal geometries. Adv. Math. 163, 206-257 (2001)
27. Gover, A.R., Šilhan, J.: In progress
28. Graham, C.R., Hirachi, K.: The ambient obstruction tensor and g-curvature. In: AdS/CFT correspondence: Einstein metrics and their conformal boundaries, pp. 59-71, IRMA Lect. Math. Theor. Phys., vol. 8, Eur. Math. Soc., ZÃijrich, 2005
29. Graham, C.R., Jenne, R., Mason, L.J., Sparling, G.A.: Conformally invariant powers of the Laplacian, I: Existence. J. London Math. Soc. 46, 557-565 (1992)
30. Paneitz, S.: A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983)
31. Riegert, R.: A nonlocal action for the trace anomaly. Phys. Lett. B 134, 56-60 (1984)
32. Thomas, T.Y.: On conformal geometry. Proc. Natl. Acad. Sci. USA 12, 352-359 (1926)
33. Wünsch, V.: On conformally invariant differential operators. Math. Nachr. 129, 269-281. (1986)