Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)
- Volume: 18, Issue: 4, page 563-629
- ISSN: 0391-173X
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topGauduchon, 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. <http://eudml.org/doc/84114>.
@article{Gauduchon1991,
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 = {http://eudml.org/doc/84114},
volume = {18},
year = {1991},
}
TY - JOUR
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 - http://eudml.org/doc/84114
ER -
References
top- [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
- [BE] A.L. Besse, Einstein manifolds, Springer Verlag, 1987, Die Ergebnisse der Mathematik 10. Zbl0613.53001MR867684
- [BB] L. Berard Bergery, La courbure scalaire des variétés riemanniennes, Séminaire Bourbaki, juin 1980, Vol. 1979/ 1980, Exp. 556. MR725678
- [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
- [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
- [BY] C.P. Boyer, A note on hyperhermitian four-manifolds, Proc. Amer. Math. Soc. 102, N. 1, Jan. 1988. Zbl0642.53073MR915736
- [DV] M. Dubois-Violette, Structures complexes au-dessus des variétés, applications, Séminaire de Mathématiques de l'ENS, 1981. Zbl0522.53029
- [FE] H.D. Fegan, Conformally invariant first order operator, Q. Jl. Math.27, 1976, p. 371-378. Zbl0334.58016MR482879
- [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
- [FO] G.B. Folland, Weyl manifolds, J. Differential Geom.4, 1970, p. 145-153. Zbl0195.23904MR264542
- [GA1] P. Gauduchon, La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann.267, 1984, p. 495-518. Zbl0523.53059MR742896
- [GA2] P. Gauduchon, Connexion canonique et géométrie conforme, Preprint.
- [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
- [HI1] N.J. Hitchin, Linear fields equations on self-dual spaces, Proc. Roy. Soc. London Ser. A, 370, 1980, p. 173-191. Zbl0436.53058MR563832
- [HI2] N.J. Hitchin, Kählerian twistor spaces, Proc. Roy. Soc. London Ser. A, 43, 1981, p. 133-150. Zbl0474.14024MR623721
- [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
- [K-N] S. Kobayashi - K. Nomizu, Foundations of Differential Geometry, Vol. 1, 1963. Interscience Publishers. Zbl0119.37502MR152974
- [K-W] S. Kobayashi - H.H. Wu, On holomorphic sections on certain hermitian vector bundles, Math. Ann.189, 1970, p. 1-4. Zbl0189.52201MR270392
- [MI] M.-L. Michelsohn, On the existence of special metrics in complex geometry, Acta Math.143, 1983, p. 261-295. Zbl0531.53053MR688351
- [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
- [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
- [PO] Y.S. Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geom.24, 1986, p. 97-132. Zbl0583.53054MR857378
- [PR] W.A. Poor, A holonomy proof of the positive curvature operator theorem, Proc. Amer. Math. Soc.79, 1980, p. 454-456. Zbl0465.53029MR567991
- [P-S] H. Pedersen- A. Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Preprint 1991. MR1199072
- [P-T] H. Pedersen, - K.P. Tod, Three-dimensional Einstein-Weyl Geometry, à paraître dans Adv. Math. Zbl0778.53041MR1200290
- [SA1] S. Salamon, Topics in four-dimensional riemannian geometry, Geometry Seminar "Luigi Bianchi" , 1983, Lecture Notes in Math. 1022, Springer Verlag. Zbl0532.53035MR728393
- [SA2] S. Salamon, Riemannian Geometry and Holonomy groups, 1989. Pitman Res. Notes Math. Ser., 201, Longman Scientific & Technical. Zbl0685.53001MR1004008
- [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
- [TA] G. Tallini, Metriche locali dotate di una connessione globale su una varietà differenziabile, Period. Mat.46, 1968, p. 340-358. Zbl0188.26002MR239533
- [TO] K.P. Tod, Compact 3-dimensional Einstein-Weyl structures, A paraître dans J. London Math. Soc. Zbl0761.53026
- [VA] I. Vaisman, On locally conformal almost Kähler manifolds, Israel J. Math.24, 1976, p. 338-351. Zbl0335.53055MR418003
- [VI] M. Ville, Twistor examples of algebraic dimension zero threefolds, Invent. Math., 10, 1991, p. 537-546. Zbl0722.32016MR1091618
- [WE] H. Weyl, Space-Times-Matter, Dover Publications (version anglaise de Raum-Zeit-Materie, Teubner, 1921). Zbl0044.22704
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