Advertisement

Mathematische Annalen

, Volume 294, Issue 1, pp 591–609 | Cite as

The deformation theory of anti-self-dual conformal structures

  • A. D. King
  • D. Kotschick
Article

Mathematics Subject Classification (1991)

58D27 58H15 58D17 53A30 32G13 58G05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AHS]
    Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond., Ser. A362, 425–461 (1978)Google Scholar
  2. [AS]
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators: III. Ann. Math.87, 546–604 (1968)Google Scholar
  3. [Be]
    Besse, A.: Einstein manifolds. Berlin Heidelberg New York: Springer 1986Google Scholar
  4. [Bo]
    Bourguignon, J.-P.: Une stratification de l'espace des structures Riemanniennes. Compos. Math.30, (Fasc. 1), 1–41 (1975)Google Scholar
  5. [DF]
    Donaldson, S.K., Friedman, R.: Connected sums of self-dual manifolds and deformations of singular spaces. Nonlinearity2, 197–239 (1989)CrossRefGoogle Scholar
  6. [E]
    Ebin, D.G.: The manifold of Riemannian metrics. In: Chern, S.-S., Smale, S. (eds.) Global analysis. (Proc. Symp. Pure Math., vol. XV, pp. 11–40) Providence, RI: Am. Math. Soc. 1970Google Scholar
  7. [FM]
    Fischer, A.E., Marsden, J.E.: The manifold of conformally equivalent metrics. Can. J. Math.XXIX (No. 1), 193–209 (1977)Google Scholar
  8. [F]
    Floer, A.: Self-dual conformal structures on ŀℂP 2. J. Differ. Geom.33, 551–573 (1991)Google Scholar
  9. [Go]
    Goldman, W.M.: Geometric structures on manifolds and varieties of representations. Contemp. Math.74, 169–198 (1988)Google Scholar
  10. [GM]
    Goldman, W.M., Millson, J.J.: The deformation theory of representations of fundamental groups of compact Kähler manifolds. Publ. Math., Inst. Hautes Étud. Sci.67, 43–96 (1988)Google Scholar
  11. [Gr]
    D'Ambra, G., Gromov, M.: Lectures on transformation groups: geometry and dynamics. Surv. Differ. Geom.1, 19–111 (1991)Google Scholar
  12. [H1]
    Hitchin, N.J.: Linear field equations on self-dual spaces. Proc. R. Soc. Lond. Ser. A370, 173–191 (1980)Google Scholar
  13. [H2]
    Hitchin, N.J.: Kählerian twistor spaces. Proc. Lond. Math. Soc., III. Ser.43, 133–150 (1981)Google Scholar
  14. [H3]
    Hitchin, N.J.: On compact four-dimensional Einstein manifolds. J. Differ. Geom.9, 435–441 (1974)Google Scholar
  15. [JM]
    Johnson, D., Millson, J.: Deformation spaces associated to compact hyperbolic manifolds. In: Howe, R. (ed.) Discrete groups in geometry and analysis. Boston Basel Stuttgart. Birkhäuser 1987Google Scholar
  16. [K]
    Kuiper, N.H.: On conformally flat spaces in the large. Ann. Math.50, 916–924 (1949)Google Scholar
  17. [L]
    LeBrun, C.: Explicit self-dual metrics on ℂP 2#...#ℂP 2. J. Differ. Geom.34, 223–254 (1991)Google Scholar
  18. [LP]
    Lee, J.M., Parker, T.H.: The Yamabe problem. Bull. Am. Math. Soc., New Ser.17 (No. 1), 37–91 (1987)Google Scholar
  19. [L-F]
    Lelong-Ferrand, J.: Transformations conformes et quasi-conformes des variétés riemanniennes, application à la démonstration d'une conjecture de A. Lichnerowicz. C.R. Acad. Sci., Paris, Sér. A269, 583–586 (1969)Google Scholar
  20. [Ob]
    Obata, M.: Conformal transformations of compact Riemannian manifolds. Ill. J. Math.6, 292–295 (1962)Google Scholar
  21. [O]
    Omori, H.: Infinite dimensional Lie transformation groups. (Lect. Notes Math., vol. 427) Berlin Heidelberg New York: Springer 1974Google Scholar
  22. [P1]
    Sun Poon, Y.: Compact self-dual manifolds with positive scalar curvature. J. Differ. Geom.24, 97–132 (1986)Google Scholar
  23. [P2]
    Sun Poon, Y.: Algebraic dimension of twistor spaces. Math. Ann.282, 621–627 (1988)CrossRefGoogle Scholar
  24. [S1]
    Salamon, S.: Topics in four-dimensional Riemannian geometry. In: Vesentini, E. (ed.) Geometry Seminar ‘Luigi Bianchi’ 1982. (Lect. Notes Math., vol. 1022) Berlin Heidelberg New York: Springer 1983Google Scholar
  25. [S2]
    Salamon, S.: Riemannian geometry and holonomy groups. (Pitman Res. Notes Math. Ser., vol. 201) Harlow Essex: Longman 1989Google Scholar
  26. [SY]
    Schoen, R., Yau, S.-T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math.92, 47–71 (1988)CrossRefGoogle Scholar
  27. [T]
    Thurston, W.P.: The geometry and topology of 3-manifolds. Princeton lecture notes (1978/79)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. D. King
    • 1
  • D. Kotschick
    • 2
  1. 1.Department of Pure MathematicsUniversity of LiverpoolLiverpoolUK
  2. 2.Mathematisches InstitutUniversität BaselBaselSwitzerland

Personalised recommendations