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Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler

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Bibliography

  1. Balas, A.: Compact Hermitian manifolds of constant holomorphic sectional curvature. (To appear)

  2. Beauville, A.: Surfaces algébriques complexes. Astérisque54, (1978)

  3. Bombieri, E., Husemoller, D.: Classification and embeddings of surfaces. Proc. Symp. Pure Math.29, 329–420 (1975)

    Google Scholar 

  4. Gauduchon, P.: La topologie d'une surface hermitienne d'Einstein. C.R. Acad. Sci. Paris290, 509–512 (1980)

    Google Scholar 

  5. Gauduchon, P.: La 1-forme de torsion d'une variété hermitienne compacte. Math. Ann.267, 495–518 (1984)

    Google Scholar 

  6. Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York-Basel: Marcel Dekker 1970

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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Balas, A., Gauduchon, P. Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler. Math Z 190, 39–43 (1985). https://doi.org/10.1007/BF01159161

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  • DOI: https://doi.org/10.1007/BF01159161

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