Self-dual Kähler manifolds and Einstein manifolds of dimension four
Compositio Mathematica, Tome 49 (1983) no. 3, pp. 405-433. 
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     author = {Derdzi\'nski, Andrzej},
     title = {Self-dual {K\"ahler} manifolds and {Einstein} manifolds of dimension four},
     journal = {Compositio Mathematica},
     pages = {405--433},
     publisher = {Martinus Nijhoff Publishers},
     volume = {49},
     number = {3},
     year = {1983},
     mrnumber = {707181},
     zbl = {0527.53030},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1983__49_3_405_0/}
}
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Derdziński, Andrzej. Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compositio Mathematica, Tome 49 (1983) no. 3, pp. 405-433. http://archive.numdam.org/item/CM_1983__49_3_405_0/

[1] T. Adati and T. Miyazawa: On a Riemannian space with recurrent conformal curvature. Tensor, N. S. 18 (1967) 348-354. | MR | Zbl

[2] M.F. Atiyah, N.J. Hitchin and I.M. Singer: Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. London A 362 (1978) 425-461. | MR | Zbl

[3] R. Bach: Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungstensorbegriffs. Math. Zeitsch. 9 (1921) 110-135. | JFM | MR

[4] L. Bérard Bergery: Sur de nouvelles variétés riemanniennes d'Einstein, preprint, Institut Elie Cartan, Université de Nancy I (1981). | MR | Zbl

[5] S. Bochner: Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52 (1946) 776-797. | MR | Zbl

[6] A. Borel: Compact Clifford-Klein forms of symmetric spaces. Topology 2 (1963) 111-122. | MR | Zbl

[7] J.P. Bourguignon: Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein. Invent. Math. 63 (1981) 263-286. | MR | Zbl

[8] E. Calabi: Extremal Kähler metrics. Seminar on Differential Geometry (edited by Shing-Tung Yau). Princeton Univ. Press and Univ. of Tokyo Press, Princeton (1982), pp. 259-290. | MR | Zbl

[9] J. Carrell, A. Howard and C. Kosniowski: Holomorphic vector fields on complex surfaces. Math. Ann. 204 (1973) 73-81. | MR | Zbl

[10] A. Derdziński: Exemples de métriques de Kähler et d'Einstein auto-duales sur le plan complexe. Géométrie riemannienne en dimension 4 (Séminaire Arthur Besse 1978/79). Cedic/Fernand Nathan, Paris (1981), pp. 334-346. | Zbl

[11] A. Derdziński and A. Rigas: Unflat connections in 3-sphere bundles over S4. Trans. Amer. Math. Soc. 265 (1981) 485-493. | MR | Zbl

[12] A. Derdziński and W. Roter: On conformally symmetric manifolds with metrics of indices 0 and 1. Tensor, N. S. 31 (1977) 255-259. | MR | Zbl

[13] D. Deturck and J.L. Kazdan: Some regularity theorems in Riemannian geometry. Ann. Sci. Ec. Norm. Sup. (4) 14 (1981) 249-260. | Numdam | MR | Zbl

[14] H. Donnelly: Topology and Einstein Kähler metrics. J. Differential Geometry 11 (1976) 259-264. | Zbl

[15] Th. Friedrich and H. Kurke: Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. Math. Nachrichten (to appear). | MR | Zbl

[16] A. Gray: Invariants of curvature operators of four-dimensional Riemannian manifolds. Proc. 13th Biennial Seminar Canadian Math. Congress (1971), vol. 2, 42-65. | MR | Zbl

[17] N. Hitchin: Compact four-dimensional Einstein manifolds. J. Differential Geometry 9 (1974) 435-441. | MR | Zbl

[18] N. Hitchin: Kählerian twistor spaces. Proc. London Math. Soc. 43 (1981 133-150. | MR | Zbl

[19] G.R. Jensen: Homogeneous Einstein spaces of dimension four. J. Differential Geometry 3 (1969) 309-349. | MR | Zbl

[20] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, vol. I. Interscience, New York (1963). | MR | Zbl

[21] A. Lichnerowicz: Espaces homogènes kählériens. Colloque de Géométrie Différentielle, Strasbourg (1953) 171-201. | MR | Zbl

[22] A. Lichnerowicz: Isométries et transformations analytiques d'une variété kählérienne compacte. Bull. Soc. Math. France 87 (1959) 427-437. | Numdam | MR | Zbl

[23] R. Mandelbaum and B. Moishezon: The topological type of algebraic surfaces: Hypersurfaces in P3(C). Proc. Symposia in Pure Math. 30 (1977), Part I, 277-283. | MR | Zbl

[24] Y. Matsushima: Remarks on Kähler-Einstein manifolds. Nagoya Math. J. 46 (1972) 161-173. | MR | Zbl

[25] J.W. Milnor and J.D. Stasheff: Characteristic Classes. Princeton University Press, Princeton (1974). | MR | Zbl

[26] D. Page: A compact rotating gravitational instanton. Phys. Lett. 79 B (1978) 235-238.

[27] A. Polombo: Nombres caractéristiques d'une surface kählérienne compacte. C. R. Acad. Sci. Paris A 283 (1976) 1025-1028. | MR | Zbl

[28] W. Roter: Some existence theorems on conformally recurrent manifolds (in preparation).

[29] I.M. Singer and J.A. Thorpe: The curvature of 4-dimensional Einstein spaces. Global Analysis, Papers in Honor of K. Kodaira, Princeton (1969) 355-365. | MR | Zbl

[30] S. Tanno: Curvature tensors and covariant derivatives. Ann. Mat. Pura Appl. 96 (1973) 233-241. | MR | Zbl

[31] J. Thorpe: Some remarks on the Gauss-Bonnet integral. J. of Math. Mech. 18 (1969) 779-786. | MR | Zbl

[32] K. Yano and I. Mogi: On real representations of Kaehlerian manifolds. Ann. of Math. 61 (1955) 170-189. | MR | Zbl

[33] S.-T. Yau: Calabi's conjecture and some new results in algebraic geometry. Proc. Natl. Acad. Sci. U.S.A. 74 (1977) 1798-1799. | MR | Zbl