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A new proof of the existence of Kähler-Einstein metrics on K3. II. (English) Zbl 0634.14026

This is the continuation of the study of Kähler Einstein metrics on \(K_ 3\) surfaces. Here the author shows that the technique used in the first part of his investigation indeed produced numerous such metrics on a \(K_ 3\) surface. Furthermore, the author points out the difference between this metric and the one constructed by T. Eguchi and A. J. Hanson [Phys. Lett. B 74, No.3, 249-251 (1978)].
Reviewer: Vo Van Tan

MSC:

14J28 \(K3\) surfaces and Enriques surfaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:

[1] [A1] Atiyah, M.: On analytic surfaces with double points. Proc. R. Soc. Lond. Ser. A247, 237-244 (1958) · Zbl 0135.21301
[2] [AHS] Atiyah, M., Hitchin, N., Singer, I.: Self-duality in four dimensional Riemannian geometry. Proc. R. Soc. Lond. Ser. A362, 425-461 (1978) · Zbl 0389.53011
[3] [B] Banica, C., Putinar, M., Schumacher, G.: Globalen Ext in Deformationen kompakter komplexer Räume. Math. Ann.250, 135-155 (1980) · Zbl 0438.32007
[4] [B-B] Beauville, A., Bourguignon, J.-P.: Géométrie des surfacesK3: modules et périodes. Astérisque126 (1985)
[5] [B-W] Burns, D., Wahl, J.: Local contributions to global deformations of surfaces. Invent. Math.26, 67-88 (1974) · Zbl 0288.14010
[6] [E-H] Eguchi T., Hanson, A.: Asymptotically flat solutions, to Euclidean, gravity. Phys. Lett. B74, 249-251 (1978)
[7] [H1] Hitchin, N.: Polygons and gravitons. Math. Proc. Camb. Philos. Soc.85, 465-476 (1979) · Zbl 0405.53016
[8] [H3] Hitchin, N.: Twistor, construction of Einstein metrics. In: Wilmore, T., Hitchin, N. (eds.), Global Riemannian geometry. New York: Halsted Press 1984
[9] [H-G] Hawking, S., Gibbons, G.: Gravitational multi-instantons. Phys. Lett. B78, 430-432 (1978)
[10] [Pg] Page, D.: A physical picture of theK3 gravitational instanton Phys. Lett. B80, 55-57 (1978)
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