Geodesic
Selfdual geometry of generalized Kählerian manifolds
Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 447-457 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complete classification has been obtained of selfdual generalized Kählerian manifolds (of both classical type and nonexceptional Kählerian manifolds of hyperbolic type) of constant scalar curvature. It has also been shown that a generalized Kählerian manifold is anti-selfdual if and only if its scalar curvature vanishes identically. These results essentially generalize well-known results of Hitchin, Bourguignon, Derdziński, Chen, and Itoh. 
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     author = {O. E. Arsen'eva},
     title = {Selfdual geometry of generalized {K\"ahlerian} manifolds},
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     volume = {79},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a11/}
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O. E. Arsen'eva. Selfdual geometry of generalized Kählerian manifolds. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 447-457. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a11/

[1] Besse A., Mnogoobraziya Einshteina, T. 1, 2, Mir, M., 1990 | MR | Zbl

[2] Penrose R., “The twistor programme”, Math. Phis. Repts., 12 (1977), 65–76 | DOI | MR

[3] Atiyah M. F., Hitchin N. J., Singer I. M., “Self-duality in four-dimensional Riemannian geometry”, Proc. Roy. London, A362 (1978), 425–461 | DOI | MR

[4] Hitchin N. J., “On compact four dimensional Einstein manifolds”, J. Diff. Geom., 9 (1974), 435–442 | MR

[5] Hitchin N. J., “Kählerian twistor space”, Proc. London Math. Soc., 43 (1981), 133–150 | DOI | MR | Zbl

[6] Chen B. J., “Some topological obstructions to Bochner–Kähler metrics and their applications”, J. Diff. Geom., 13 (1978), 547–558 | MR | Zbl

[7] Bourguignon J. P., “Les varietes de dimension $4$ a signature non nulle dont la courbure est harmonique sont d$'$Einstein”, Invent Math., 63 (1981), 263–286 | DOI | MR | Zbl

[8] Derdzinski A., “Self-dual Kähler manifolds and Einstein manifolds of dimensional four”, Comp. Math., 49 (1983), 405–433 | MR | Zbl

[9] Itoh M., “Self-duality of Kähler surfaces”, Comp. Math., 51 (1984), 265–273 | MR | Zbl

[10] “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhn. Problemy geometrii, 18, VINITI AN SSSR, 1986, 25–72

[11] Kirichenko V. F., “$K$-prostranstva postoyannoi golomorfnoi sektsionnoi krivizny”, Matem. zametki, 19:5 (1976), 805–814 | MR | Zbl

[12] Kirichenko V. F., “Aksioma golomorfnykh ploskostei v obobschennoi ermitovoi geometrii”, DAN SSSR, 260:4 (1981), 795–799 | MR | Zbl

[13] Chetyrekhmernaya rimanova geometriya, Seminar Artura Besse 1978–1979, Mir, M., 1985 | MR

[14] Lichnerowicz A., “Spineurs harmoniques”, C. R. Acad. Sci. Paris, 257 (1963), 7–9 | MR | Zbl

[15] Kazdan J. L., Warner J. W., “A direct approach to the determination of Gaussian and scalar curvature function”, Invent Math., 28 (1975), 227–230 | DOI | MR | Zbl

[16] Kodaira K., “On the structure of compact complex analytic surfaces, I”, Amer. J. Math., 86 (1964), 751–798 | DOI | MR | Zbl