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Conformal duality and compact complex surfaces

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References

  1. Atiyah, M.F.: Geometry of Yang-Mills fields. Academia Nazionale dei Lincei, Scuola Normale Superiore, Pisa (1979)

    Google Scholar 

  2. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. Lond. A362, 425–461 (1978)

    Google Scholar 

  3. Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. New York: Springer 1984

    Google Scholar 

  4. Bourguigon, J.P.: Les varietés de dimension 4 a signature non nulle dont la courbure est harmonique sont d'Einstein. Invent. Math.63, 263–286 (1981)

    Article  Google Scholar 

  5. Derdzinski, A.: Hermitian Einstein metrics. In: Global Riemannian geometry. Ed. Willmore, T.J., Hitchin, N.J. pp. 105–114

  6. Derdzinski, A.: Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compos. Math.49, 405–433 (1983)

    Google Scholar 

  7. Gauduchon, P.: Fibrés Hermitiens a endomorphisme de Ricci non negatif. Bull. Soc. Math. France105, 113–140 (1970)

    Google Scholar 

  8. Gauduchon, P.: Le théorème de l'excentricité nulle. C.R. Acad. Sci. Paris285, 387–390 (1977)

    Google Scholar 

  9. Goldberg, S.I.: Curvature and homology. New York: Academic Press 1962

    Google Scholar 

  10. Gromov, M., Lawson, H.B.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. Math. Inst. Haustes Etud. Sci.58, 295–408 (1983)

    Google Scholar 

  11. Hitchin, N.: Compact Four-dimensional Einstein Manifolds. J. Differ. Geom.9, 435–441 (1974)

    Google Scholar 

  12. Hitchin, N.: Harmonic spinors. Adv. Math.14, 1–55 (1974)

    Google Scholar 

  13. Ibrahim, J., Lichnerowicz, A.: Tenseurs holomorphes sur une variéte kahlérienne compacte. C.R. Acad. Sci. Paris,277, 801–805 (1973)

    Google Scholar 

  14. Itoh, M.: Self-duality of Kähler surfaces. Compos. Math.51, 265–273 (1984)

    Google Scholar 

  15. Kazdan, J.L., Warner, F.W.: Prescribing curvature. Proc. Symp. Pure Math27, 309–319 (1973)

    Google Scholar 

  16. Kodaira, K.: On the structure of compact complex analytic surfaces. I. Am. J. Math.86, 751–798 (1964)

    Google Scholar 

  17. Lafontaine, J.: Remarques sur les varietes conforment plates. Math. Ann.259, 313–319 (1982)

    Google Scholar 

  18. Lichnerowicz, A.: Spineurs harmoniques. C.R. Acad. Sci. Paris, sér, A-B257, 7–9 (1963)

    Google Scholar 

  19. Schoen, R., Yau, S.T.: On the structure of manifolds with positive scalar curvature, Manuscr. Math.28, 159–183 (1979)

    Google Scholar 

  20. Singer, I.M., Thorpe, J.A.: The curvature of 4-dimensional Einstein spaces. In: Global analysis, papers in honor of K. Kodaira. Eds. Spencer, D.C., Iyanaga, S., pp. 355–365

  21. Strominger, A., Horowitz, G.T., Perry, M.J.: Instantons in conformal gravity. Nucl. Phys.B 238, 635–664 (1984)

    Google Scholar 

  22. Vaisman, I.: Some curvature properties of complex surfaces, Ann. Mat. Para Appl.32, 1–18 (1982)

    Google Scholar 

  23. Vaisman, I.: Generalized Hopf manifolds. Geom. Dedicata13, 231–255 (1982)

    Google Scholar 

  24. Vaisman, I.: On locally and globally conformal Kähler manifolds. Trans. Am. Math. Soc.262, 533–542 (1980)

    Google Scholar 

  25. Yano, K., Bochner, S.: Curvature and Betti numbers. Princeton: Princeton Univ. Press 1953

    Google Scholar 

  26. Yau, S.T.: On the curvature of compact Hermitian manifolds. Invent. Math.25, 213–239 (1974)

    Google Scholar 

  27. Yau, S.T. (Ed.) Seminar on differential geometry. Princeton Princeton Univ. Press 1982

    Google Scholar 

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  1. Department of Mathematics and Computer Science, Clarkson University, 13676, Potsdam, NY, USA

    Charles P. Boyer

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  1. Charles P. Boyer
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Boyer, C.P. Conformal duality and compact complex surfaces. Math. Ann. 274, 517–526 (1986). https://doi.org/10.1007/BF01457232

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