Variétés riemanniennes autoduales

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1. [A-K-L] M. Anderson, P.B. Kronheimer, C. LeBrun. Complete Ricci-flat Kähler manifolds of infinite topological type. Comm. Math. Phys.125 (1989), 643-660. Zbl0734.53051MR1024931
2. [At] M.F. Atiyah. The geometry of Yang-Mills fields. Lezioni Fermiane. Scuola Superiore Pisa. 1979. Zbl0435.58001MR554924
3. [A-H-S] M.F. Atiyah, N.J. Hitchin, I.M. Singer. Self-duality in four-dimensional Riemannian Geometry. Proc. R. Soc. Lond. A362 (1978), 425-461. Zbl0389.53011MR506229
4. [Ba-Ea] R.J. Baston, M.G. Eastwood. The Penrose Transform. Its Interaction with Representation Theory. Clarendon Press. Oxford. 1989. Zbl0726.58004MR1038279
5. [Be1] A.L. Besse. Géométrie riemannienne en dimension4 (1981). Cedic-F. Nathan. MR769127
6. [Be2] A.L. Besse. Einstein manifolds. Ergebnisse der Math.10, 1987, Springer. Zbl0613.53001MR867684
7. [Bo] J.P. Bourguignon. Stabilité par déformation non-linéaire de la métrique de Minkowski. Séminaire Bourbaki n°740 Juin 1991Astérisque201- 202-209. Zbl0754.53060MR1157847
8. [Ca] F. Campana. On twistor spaces of the class C. J. Diff. Geom.33 (1991), 541-549. Zbl0694.32017MR1094468
9. [De] A. Derdzinski. Self-dual Kähler manifolds and Einstein manifolds of dimension four. Comp. Math.49 (1983), 405-433. Zbl0527.53030MR707181
10. [Do] S.K. Donaldson. An application of gauge theory to four-dimensional topology. J. Diff. Geom.18 (1983), 279-315. Zbl0507.57010MR710056
11. [Do-Kr] S.K. Donaldson, P.B. Kronheimer. The Geometry of Four-Manifolds. Clarendon Press. Oxford. 1990. Zbl0820.57002MR1079726
12. [Do-Ve] A. Douady - J.L. Verdier. Les équations de Yang-MillsSéminaire ENS77-78, Astérisque71-72. Zbl0457.14009MR589891
13. [DV] M. Dubois-Violette. Structures complexes au-dessus des variétés, applications. dans : "Mathématiques et physique" Séminaire de l'E.N.S.79-82, Ed. L. Boutet de Monvel, A. Douady, J.L. Verdier. Prog. in Math.37 (1983) Birkhäuser. (1981). Zbl0522.53029MR728412
14. [Do-Fr] S.K. Donaldson, R. Friedman. Connected sum of self-dual manifolds and deformations of singular spaces. Nonlinearity2 (1989), 197-239. Zbl0671.53029MR994091
15. [Ea-Le] M.G. Eastwood - C. LeBrun. Fattening complex manifolds : curvature and Kodaira-Spencer maps. J. Geom. Phys.8 (1992), 123-146. Zbl0748.32017MR1165875
16. [E-P-W] M.G. Eastwood, R. Penrose, R.O. Wells, Jr. Cohomology and massless fields. Comm. Math. Phys.78 (1981), 305-351. Zbl0465.58031MR603497
17. [E-G-H] T. Eguchi, P.B. Gilkey, A.J. Hanson. Gravitation, Gauge theories and Differential Geometry. Phys. Reports66 (1980), 215-397. MR598586
18. [Fl] A. Floer. Self-dual conformal structures on lCP2. J. Diff. Geom.33 (1991), 551-573. Zbl0736.53046MR1094469
19. [Fr] M.H. Freedman. The topology of four-dimensional manifolds. J. Diff. Geom.17 (1992), 357-454. Zbl0528.57011MR679066
20. [Fr-Ku] T. Friedrich - H. Kurke. Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. MathNachr.106 (1982), 271- 299. Zbl0503.53035MR675762
21. [Fr-Uh] D.S. Fried - K.K. Uhlenbeck. Instantons and four-manifoldsMSRI Publ. Vol. 1 (1984). Springer. Zbl0559.57001MR757358
22. [Ga] P. Gauduchon. Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale. Ann. Scuola Norm. Sup. Pisa XVIII (1991), 563-629. Zbl0763.53034MR1153706
23. [Gi-Ha] G.W. Gibbons - S.W. Hawking. Gravitational multi-instantons. Phys. Lett. B.78 (1978), 430-432. 
24. [Hi1] N.J. Hitchin. Polygons and Gravitons. Math. Proc. Camb. Phil. Soc.83, (1979), 465-476. Zbl0405.53016MR520463
25. [Hi2] N.J. Hitchin. Linear field equations on self-dual spaces. Proc. R. Soc. Lond. A370 (1980), 173-191. Zbl0436.53058MR563832
26. [Hi3] N.J. Hitchin. Kählerian Twistor SpacesProc. R. Soc. Lond.43 (1981), 133-150. Zbl0474.14024MR623721
27. [Hi4] N.J. Hitchin. The Yang-Mills equation and the topology of four-manifolds [d'après S.K. Donaldson], Séminaire Bourbaki n° 606, fév. 1983Astérique105-106. Zbl0533.57007MR728987
28. [Hi5] N.J. Hitchin. Hyperkähler manifolds. Séminaire Bourbaki n°748 nov. 1991. 
29. [Hu] J. Hurtubise. The intersection of two quadrics in P5(C) as a twistor space. Ann. Glob. Analysis Geom. Vol. 3 (1985), 185-195. Zbl0579.32048MR809637
30. [Itl] M. Itoh. Half-conformally Flat Structures and the Deformation Obstruction Space. A paraître dans Math. J. Tsukuba. Zbl0809.53038
31. [It2] M. Itoh. Moduli of Half Conformally Flat Structures. A paraître aux Math. Ann.. Zbl0788.58011MR1233492
32. [Ko] K. Kodaira. A theorem of completness of characteristic systems for analytic families of compact submanifolds of a complex manifold. Ann. of Math.75 (1962), 146-162. Zbl0112.38404MR133841
33. [Ki-Ko] A.D. King - D. Kotschick. The deformation theory of anti-self-dual conformal structures. Math. Ann.294 (1992), 591-609. Zbl0765.58005MR1190446
34. [Ki-Po] J. Kim - M. Pontecorvo. A new method of constructing scalar-flat Kähler metrics (1993). Preprint. 
35. [Kr-Ku] B. Kreussler - H. Kurke. Twistor spaces over the connected sum of 3 projective planes. Comp. Math.82 (1992), 25-55. Zbl0766.53049MR1154160
36. [Ku] H. Kurke. Classification of twistor spaces with a pencil of surfaces of degree 1, I. A paraître aux Math. Nachr. Zbl0820.53052MR1235296
37. [La] J. Lafontaine. Remarques sur les variétés conformément plates. Math. Ann.259 (1982), 313-319. Zbl0469.53036MR661199
38. [Le1] C. LeBrun. Scalar-flat Kähler matrics. J. reine angew. Math.420 (1991), 161-172. Zbl0727.53067MR1124569
39. [Le2] C. LeBrun. Explicit self-dual metrics on CP2#...#CP2. J. Diff. Geom.34 (1991), 233-253. Zbl0725.53067MR1114461
40. [Le3] C. LeBrun. Asymptotically-Flat Scalar Kähler Surfaces. Preprint. 
41. [Le-Si 1] C. LeBrun - M.A. Singer. Existence and Deformation Theory for Scalar-Flat Kähler Metrics on Compact Complex Surfaces. Inv. Math.112 (1993), 273-313. Zbl0793.53067MR1213104
42. [Le-Si 2] C. LeBrun - M.A. Singer. A Kummer-type construction of self-dual 4-manifolds (1993). Preprint. 
43. [Lw] H. Blaine Lawson, Jr. The theory of gauge fields in four dimensions. CBMS58 (1985). Zbl0597.53001
44. [Pe1] R. Penrose. Non-linear gravitons and curved twistor theory. Gen. Relativity Grav.7 (1976), 31-52. Zbl0354.53025MR439004
45. [Pe2] R. Penrose. The complex Geometry of the Natural Word. Proc. Intern. Congress Math. Helsinki, (1978). Zbl0425.53033
46. [Pe3] R. Penrose. On the origin of twistor theory. in : Gravitation and Geometry, in honour of I. Robinson, ed. W. Rindler and A. Trautman. Bibliopolis, Naples (1987). Zbl0656.53005MR938546
47. [Pe-Ri] R. Penrose - W. Rindler. Spinors and Space-time 1,2. Cambridge U. Press (1984-1986). Zbl0591.53002
48. [Po1] Y.S. Poon. Compact self-dual manifolds with positive scalar curvature. J. Diff. Geom.24 (1986), 97-132. Zbl0583.53054MR857378
49. [Po2] Y.S. Poon. Algebraic dimension of twistor spaces. Math. Ann.282 (1988), 621-627. Zbl0665.32014MR970223
50. [Pn1] M. Pontecorvo. Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics. Math. Ann.291 (1991), 113-122. Zbl0747.32021MR1125011
51. [Pn2] M. Pontecorvo. Twistor spaces of anti-self-dual Hermitian surfaces. Trans. Am. Math. Soc.331 (1992), 653-661. Zbl0754.53053MR1050087
52. [Pr] M.J. Perry. Gravitational instantons, in : Seminar on Differential Geometry, Ed. S.T. Yau (1982), Princeton U. Press102. Zbl0477.53064MR645760
53. [Sa] S. Salamon. Topics in f our-dimensional Riemannian Geometry. Geometry Seminar "Luigi Bianchi" (1982). Ed.E. Vesentini. LNM1022. Springer. Zbl0532.53035
54. [Si] C.T. Simpson. Higgs bundles and local systems. Publ. math. IHES n°75 (1992), 5-95. Zbl0814.32003MR1179076
55. [Si-Th] I.M. Singer - J.A. Thorpe. The curvature of 4-dimensional Einstein spaces. Global Analysis. Papers in honour of K. Kodaira. Ed. D.C. Spencer and S.I. Iyanaga (1969) Princeton Math. Series 29. Zbl0199.25401MR256303
56. [Ta1] C.H. Taubes. Self-dual Yang-Mills connections on non-self-dual 4- manifolds. J. Diff. Geom.17 (1982), 139-170. Zbl0484.53026MR658473
57. [Ta2] C.H. Taubes. Self-dual connections on 4-manifolds with indefinite intersection metrics. J. Diff. Geom.19 (1984), 517-560. Zbl0552.53011MR755237
58. [Ta3] C.H. Taubes. The stable topology of self-dual moduli spaces. J. Diff. Geom.29 (1989), 163-230. Zbl0669.58005MR978084
59. [Ta4] C.H. Taubes. The existence of anti-self-dual conformal structures. J. Diff. Geom.36 (1992), 163-253. Zbl0822.53006MR1168984
60. [TN] Twistor Newsletter (périodique). Mathematical Institute. Oxford. 
61. [To] P. Topiwalla. A new proof of the existence of Kähler-Einstein metrics on K3, I, II. Inv. Math.89 (1987), 425-454. Zbl0634.14026MR894388
62. [Vi] M. Ville. Twistor examples of algebraic dimension zero threefolds. Inv. Math.10 (1991), 537-546. Zbl0722.32016MR1091618
63. [Ya1] S.T. Yau. On the Curvature of Compact Hermitian Manifolds. Inv. Math.25 (1974), 213-239. Zbl0299.53039MR382706
64. [Ya2] S.T. Yau. Calabi's conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA74 (1977), 1798-1799. Zbl0355.32028MR451180

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