Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale

Paul Gauduchon

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)

  • Volume: 18, Issue: 4, page 563-629
  • ISSN: 0391-173X

How to cite


Gauduchon, Paul. "Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.4 (1991): 563-629. <>.

author = {Gauduchon, Paul},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {conformal structure; twistor space; Gauduchon metric; Weitzenböck type; conformal class},
language = {fre},
number = {4},
pages = {563-629},
publisher = {Scuola normale superiore},
title = {Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale},
url = {},
volume = {18},
year = {1991},

AU - Gauduchon, Paul
TI - Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 4
SP - 563
EP - 629
LA - fre
KW - conformal structure; twistor space; Gauduchon metric; Weitzenböck type; conformal class
UR -
ER -


  1. [A-H-S] M.F. Atiyah - N.J. Hitchin - I.M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A, 1978, p. 425-461. Zbl0389.53011MR506229
  2. [BE] A.L. Besse, Einstein manifolds, Springer Verlag, 1987, Die Ergebnisse der Mathematik 10. Zbl0613.53001MR867684
  3. [BB] L. Berard Bergery, La courbure scalaire des variétés riemanniennes, Séminaire Bourbaki, juin 1980, Vol. 1979/ 1980, Exp. 556. MR725678
  4. [BO1] J.P. Bourguignon, Yang-Mills theory: the differential geometric side, in Differential Geometry (Proceedings, Lyngby1985, V.L. HANSEN (Ed.), Lecture Notes in Math.1263, Springer Verlag. Zbl0621.53028MR905878
  5. [BO2] J.P. Bourguignon, The "magic" of Weitzenböck formulas in Variational Methods. Progress in non-linear differential equations and their applications4, Birkhäuser, 1990. Zbl0774.35003MR1205158
  6. [BY] C.P. Boyer, A note on hyperhermitian four-manifolds, Proc. Amer. Math. Soc. 102, N. 1, Jan. 1988. Zbl0642.53073MR915736
  7. [DV] M. Dubois-Violette, Structures complexes au-dessus des variétés, applications, Séminaire de Mathématiques de l'ENS, 1981. Zbl0522.53029
  8. [FE] H.D. Fegan, Conformally invariant first order operator, Q. Jl. Math.27, 1976, p. 371-378. Zbl0334.58016MR482879
  9. [F-K] T. Friedrich - H. Kurke, Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature, Math. Nachr.106, 1982, p. 271-299. Zbl0503.53035MR675762
  10. [FO] G.B. Folland, Weyl manifolds, J. Differential Geom.4, 1970, p. 145-153. Zbl0195.23904MR264542
  11. [GA1] P. Gauduchon, La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann.267, 1984, p. 495-518. Zbl0523.53059MR742896
  12. [GA2] P. Gauduchon, Connexion canonique et géométrie conforme, Preprint. 
  13. [G-M] S. Gallot - D. Meyer, Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne, J. Math. Pures Appl.54, 1975, p. 259-284. Zbl0316.53036MR454884
  14. [HI1] N.J. Hitchin, Linear fields equations on self-dual spaces, Proc. Roy. Soc. London Ser. A, 370, 1980, p. 173-191. Zbl0436.53058MR563832
  15. [HI2] N.J. Hitchin, Kählerian twistor spaces, Proc. Roy. Soc. London Ser. A, 43, 1981, p. 133-150. Zbl0474.14024MR623721
  16. [HI3] N.J. Hitchin, Complex manifolds and Einstein equations, in Twistor Geometry and Non-linear Systems (Proceedings Primorsko, 1980), ed. by H.D. DOEBNER and T.D. PALEV, Lecture Notes in Math. 970, Springer Verlag. Zbl0507.53025MR699802
  17. [K-N] S. Kobayashi - K. Nomizu, Foundations of Differential Geometry, Vol. 1, 1963. Interscience Publishers. Zbl0119.37502MR152974
  18. [K-W] S. Kobayashi - H.H. Wu, On holomorphic sections on certain hermitian vector bundles, Math. Ann.189, 1970, p. 1-4. Zbl0189.52201MR270392
  19. [MI] M.-L. Michelsohn, On the existence of special metrics in complex geometry, Acta Math.143, 1983, p. 261-295. Zbl0531.53053MR688351
  20. [MU] O. Mushkarov, Structures presque-complexes sur des espaces twistoriels et leurs types, C.R. Acad. Sci. Paris, 305, 1, 1987, p. 307-309. Zbl0626.53028MR910366
  21. [PL] A. Polombo, Condition d'Einstein et courbure négative en dimension 4, C.R. Acad. Sci. Paris, 307, I, 1988, p. 667-670. Zbl0647.53038MR967809
  22. [PO] Y.S. Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geom.24, 1986, p. 97-132. Zbl0583.53054MR857378
  23. [PR] W.A. Poor, A holonomy proof of the positive curvature operator theorem, Proc. Amer. Math. Soc.79, 1980, p. 454-456. Zbl0465.53029MR567991
  24. [P-S] H. Pedersen- A. Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Preprint 1991. MR1199072
  25. [P-T] H. Pedersen, - K.P. Tod, Three-dimensional Einstein-Weyl Geometry, à paraître dans Adv. Math. Zbl0778.53041MR1200290
  26. [SA1] S. Salamon, Topics in four-dimensional riemannian geometry, Geometry Seminar "Luigi Bianchi" , 1983, Lecture Notes in Math. 1022, Springer Verlag. Zbl0532.53035MR728393
  27. [SA2] S. Salamon, Riemannian Geometry and Holonomy groups, 1989. Pitman Res. Notes Math. Ser., 201, Longman Scientific & Technical. Zbl0685.53001MR1004008
  28. [S-T] LM. Singer- J.A. Thorpe, The curvature of 4-dimensional Einstein spaces, in Global Analysis. Papers in honour of Kunihiko Kodaira, ed. by D.C. SPENCER and S.I. IYANAGA, 1969, Princeton Math. Ser. 29. Zbl0199.25401
  29. [TA] G. Tallini, Metriche locali dotate di una connessione globale su una varietà differenziabile, Period. Mat.46, 1968, p. 340-358. Zbl0188.26002MR239533
  30. [TO] K.P. Tod, Compact 3-dimensional Einstein-Weyl structures, A paraître dans J. London Math. Soc. Zbl0761.53026
  31. [VA] I. Vaisman, On locally conformal almost Kähler manifolds, Israel J. Math.24, 1976, p. 338-351. Zbl0335.53055MR418003
  32. [VI] M. Ville, Twistor examples of algebraic dimension zero threefolds, Invent. Math., 10, 1991, p. 537-546. Zbl0722.32016MR1091618
  33. [WE] H. Weyl, Space-Times-Matter, Dover Publications (version anglaise de Raum-Zeit-Materie, Teubner, 1921). Zbl0044.22704

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.