Variétés riemanniennes autoduales [d'après C.H. Taubes et al.]

Gauduchon, Paul

Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 767, 36 p.

MR Zbl | 3 citations dans Numdam

@incollection{SB_1992-1993__35__151_0,
     author = {Gauduchon, Paul},
     title = {Vari\'et\'es riemanniennes autoduales [d'apr\`es {C.H.} {Taubes} et al.]},
     booktitle = {S\'eminaire Bourbaki : volume 1992/93, expos\'es 760-774},
     series = {Ast\'erisque},
     note = {talk:767},
     pages = {151--186},
     year = {1993},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {216},
     mrnumber = {1246397},
     zbl = {0789.53026},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1992-1993__35__151_0/}
}

TY  - CHAP
AU  - Gauduchon, Paul
TI  - Variétés riemanniennes autoduales [d'après C.H. Taubes et al.]
BT  - Séminaire Bourbaki : volume 1992/93, exposés 760-774
AU  - Collectif
T3  - Astérisque
N1  - talk:767
PY  - 1993
SP  - 151
EP  - 186
IS  - 216
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/SB_1992-1993__35__151_0/
LA  - fr
ID  - SB_1992-1993__35__151_0
ER  -

%0 Book Section
%A Gauduchon, Paul
%T Variétés riemanniennes autoduales [d'après C.H. Taubes et al.]
%B Séminaire Bourbaki : volume 1992/93, exposés 760-774
%A Collectif
%S Astérisque
%Z talk:767
%D 1993
%P 151-186
%N 216
%I Société mathématique de France
%U https://www.numdam.org/item/SB_1992-1993__35__151_0/
%G fr
%F SB_1992-1993__35__151_0

Gauduchon, Paul. Variétés riemanniennes autoduales [d'après C.H. Taubes et al.], dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 767, 36 p.. https://www.numdam.org/item/SB_1992-1993__35__151_0/

Bibliographie
Cité par

[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. | Zbl | MR

[At] M. F. Atiyah. The geometry of Yang-Mills fields. Lezioni Fermiane. Scuola Superiore Pisa. 1979. | Zbl | MR

[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. | Zbl | MR

[Ba-Ea] R. J. Baston, M. G. Eastwood. The Penrose Transform. Its Interaction with Representation Theory. Clarendon Press. Oxford. 1989. | Zbl | MR

[Be1] A. L. Besse. Géométrie riemannienne en dimension 4 (1981). Cedic-F. Nathan. | MR

[Be2] A. L. Besse. Einstein manifolds. Ergebnisse der Math. 10, 1987, Springer. | Zbl | MR

[Bo] J. P. Bourguignon. Stabilité par déformation non-linéaire de la métrique de Minkowski. Séminaire Bourbaki n°740 Juin 1991 Astérisque 201- 202-209. | Zbl | MR | Numdam | EuDML

[Ca] F. Campana. On twistor spaces of the class C. J. Diff. Geom. 33 (1991), 541-549. | Zbl | MR

[De] A. Derdzinski. Self-dual Kähler manifolds and Einstein manifolds of dimension four. Comp. Math. 49 (1983), 405-433. | Zbl | MR | Numdam | EuDML

[Do] S. K. Donaldson. An application of gauge theory to four-dimensional topology. J. Diff. Geom. 18 (1983), 279-315. | Zbl | MR

[Do-Kr] S. K. Donaldson, P. B. Kronheimer. The Geometry of Four-Manifolds. Clarendon Press. Oxford. 1990. | Zbl | MR

[Do-Ve] A. Douady - J. L. Verdier. Les équations de Yang-Mills Séminaire ENS 77-78, Astérisque 71-72. | Zbl | MR

[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). | Zbl | MR

[Do-Fr] S. K. Donaldson, R. Friedman. Connected sum of self-dual manifolds and deformations of singular spaces. Nonlinearity 2 (1989), 197-239. | Zbl | MR

[Ea-Le] M. G. Eastwood - C. Lebrun. Fattening complex manifolds : curvature and Kodaira-Spencer maps. J. Geom. Phys.8 (1992), 123-146. | Zbl | MR

[E-P-W] M. G. Eastwood, R. Penrose, R. O. Wells, Jr. Cohomology and massless fields. Comm. Math. Phys. 78 (1981), 305-351. | Zbl | MR

[E-G-H] T. Eguchi, P. B. Gilkey, A. J. Hanson. Gravitation, Gauge theories and Differential Geometry. Phys. Reports 66 (1980), 215-397. | MR

[Fl] A. Floer. Self-dual conformal structures on lCP2. J. Diff. Geom. 33 (1991), 551-573. | Zbl | MR

[Fr] M. H. Freedman. The topology of four-dimensional manifolds. J. Diff. Geom. 17 (1992), 357-454. | Zbl | MR

[Fr-Ku] T. Friedrich - H. Kurke. Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. MathNachr. 106 (1982), 271- 299. | Zbl | MR

[Fr-Uh] D. S. Fried - K. K. Uhlenbeck. Instantons and four-manifolds MSRI Publ. Vol. 1 (1984). Springer. | Zbl | MR

[Ga] P. Gauduchon. Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale. Ann. Scuola Norm. Sup. Pisa XVIII (1991), 563-629. | Zbl | MR | Numdam

[Gi-Ha] G. W. Gibbons - S. W. Hawking. Gravitational multi-instantons. Phys. Lett. B. 78 (1978), 430-432.

[Hi1] N. J. Hitchin. Polygons and Gravitons. Math. Proc. Camb. Phil. Soc. 83, (1979), 465-476. | Zbl | MR

[Hi2] N. J. Hitchin. Linear field equations on self-dual spaces. Proc. R. Soc. Lond. A370 (1980), 173-191. | Zbl | MR

[Hi3] N. J. Hitchin. Kählerian Twistor Spaces Proc. R. Soc. Lond. 43 (1981), 133-150. | Zbl | MR

[Hi4] N. J. Hitchin. The Yang-Mills equation and the topology of four-manifolds [d'après S.K. Donaldson], Séminaire Bourbaki n° 606, fév. 1983 Astérique 105-106. | Zbl | MR | Numdam

[Hi5] N. J. Hitchin. Hyperkähler manifolds. Séminaire Bourbaki n°748 nov. 1991. | Numdam

[Hu] J. Hurtubise. The intersection of two quadrics in P5(C) as a twistor space. Ann. Glob. Analysis Geom. Vol. 3 (1985), 185-195. | Zbl | MR

[Itl] M. Itoh. Half-conformally Flat Structures and the Deformation Obstruction Space. A paraître dans Math. J. Tsukuba. | Zbl

[It2] M. Itoh. Moduli of Half Conformally Flat Structures. A paraître aux Math. Ann.. | Zbl | MR

[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. | Zbl | MR

[Ki-Ko] A. D. King - D. Kotschick. The deformation theory of anti-self-dual conformal structures. Math. Ann. 294 (1992), 591-609. | Zbl | MR

[Ki-Po] J. Kim - M. Pontecorvo. A new method of constructing scalar-flat Kähler metrics (1993). Preprint.

[Kr-Ku] B. Kreussler - H. Kurke. Twistor spaces over the connected sum of 3 projective planes. Comp. Math. 82 (1992), 25-55. | Zbl | MR | Numdam

[Ku] H. Kurke. Classification of twistor spaces with a pencil of surfaces of degree 1, I. A paraître aux Math. Nachr. | Zbl | MR

[La] J. Lafontaine. Remarques sur les variétés conformément plates. Math. Ann. 259 (1982), 313-319. | Zbl | MR

[Le1] C. Lebrun. Scalar-flat Kähler matrics. J. reine angew. Math. 420 (1991), 161-172. | Zbl | MR

[Le2] C. Lebrun. Explicit self-dual metrics on CP2#...#CP2. J. Diff. Geom. 34 (1991), 233-253. | Zbl | MR

[Le3] C. Lebrun. Asymptotically-Flat Scalar Kähler Surfaces. Preprint.

[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. | Zbl | MR

[Le-Si 2] C. Lebrun - M. A. Singer. A Kummer-type construction of self-dual 4-manifolds (1993). Preprint.

[Lw] H. Blaine Lawson, Jr. The theory of gauge fields in four dimensions. CBMS 58 (1985). | Zbl

[Pe1] R. Penrose. Non-linear gravitons and curved twistor theory. Gen. Relativity Grav. 7 (1976), 31-52. | Zbl | MR

[Pe2] R. Penrose. The complex Geometry of the Natural Word. Proc. Intern. Congress Math. Helsinki, (1978). | Zbl

[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). | Zbl | MR

[Pe-Ri] R. Penrose - W. Rindler. Spinors and Space-time 1,2. Cambridge U. Press (1984-1986). | Zbl

[Po1] Y. S. Poon. Compact self-dual manifolds with positive scalar curvature. J. Diff. Geom. 24 (1986), 97-132. | Zbl | MR

[Po2] Y. S. Poon. Algebraic dimension of twistor spaces. Math. Ann. 282 (1988), 621-627. | Zbl | MR

[Pn1] M. Pontecorvo. Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics. Math. Ann. 291 (1991), 113-122. | Zbl | MR

[Pn2] M. Pontecorvo. Twistor spaces of anti-self-dual Hermitian surfaces. Trans. Am. Math. Soc. 331 (1992), 653-661. | Zbl | MR

[Pr] M. J. Perry. Gravitational instantons, in : Seminar on Differential Geometry, Ed. S.T. Yau (1982), Princeton U. Press 102. | Zbl | MR

[Sa] S. Salamon. Topics in f our-dimensional Riemannian Geometry. Geometry Seminar "Luigi Bianchi" (1982). Ed.E. Vesentini. LNM 1022. Springer. | Zbl

[Si] C. T. Simpson. Higgs bundles and local systems. Publ. math. IHES n°75 (1992), 5-95. | Zbl | MR | Numdam

[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. | Zbl | MR

[Ta1] C. H. Taubes. Self-dual Yang-Mills connections on non-self-dual 4- manifolds. J. Diff. Geom. 17 (1982), 139-170. | Zbl | MR

[Ta2] C. H. Taubes. Self-dual connections on 4-manifolds with indefinite intersection metrics. J. Diff. Geom. 19 (1984), 517-560. | Zbl | MR

[Ta3] C. H. Taubes. The stable topology of self-dual moduli spaces. J. Diff. Geom. 29 (1989), 163-230. | Zbl | MR

[Ta4] C. H. Taubes. The existence of anti-self-dual conformal structures. J. Diff. Geom. 36 (1992), 163-253. | Zbl | MR

[TN] Twistor Newsletter (périodique). Mathematical Institute. Oxford.

[To] P. Topiwalla. A new proof of the existence of Kähler-Einstein metrics on K3, I, II. Inv. Math. 89 (1987), 425-454. | Zbl | MR

[Vi] M. Ville. Twistor examples of algebraic dimension zero threefolds. Inv. Math. 10 (1991), 537-546. | Zbl | MR

[Ya1] S. T. Yau. On the Curvature of Compact Hermitian Manifolds. Inv. Math. 25 (1974), 213-239. | Zbl | MR

[Ya2] S. T. Yau. Calabi's conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA 74 (1977), 1798-1799. | Zbl | MR