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On the curvature of compact Hermitian manifolds

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References

  1. Andreotti, A.: On the complex structures of a class of simply-connected manifolds. In: Algebraic Geometry and Topology; A Symposium in Honor of S. Lefschetz, Princeton University Press, Princeton, N. J., pp. 53–77, 1957

    Google Scholar 

  2. Atiyah, M.F.: Complex fiber bundles and ruled surfaces. Proc. London Math. Soc.5, 407–434 (1955)

    Google Scholar 

  3. Aubin, T.: Metriques Riemanniennes et courbure. J. Differential Geometry4, 383–424 (1970)

    Google Scholar 

  4. Bloch, S., Gieseker, D.: The positivity of the Chern classes of an ample vector bundle. Inventiones math.12, 112–117 (1971)

    Google Scholar 

  5. Bott, R.: Vector fields and characteristic numbers. Mich. Math. J.14, 231–244 (1967)

    Google Scholar 

  6. Chern, S.S.: On holomorphic mappings of Hermitian manifolds of the same dimension. In: Proc. Symp. Pure Math. 11, Amer. Math. Soc., Providence, R.I., pp. 157–170, 1968

  7. Frankel, T.: Manifolds with positive curvature. Pacific J. Math.11, 165–174 (1961)

    Google Scholar 

  8. Frankel, T.: Fixed points and torsions of Kähler manifolds. Ann. of Math.70, 1–8 (1959)

    Google Scholar 

  9. Griffiths, P.: Holomorphic mappings into canonical algebraic varieties. Ann. of Math.93, 439–458 (1971)

    Google Scholar 

  10. Griffiths, P.: Hermitian differential geometry, Chern classes, and positive vector bundles. In: Global Analysis, Princeton Math. Series29, 185–251 (1969)

  11. Hartshorne, R.: Ample subvarieties of algebraic varieties. In: Lecture Notes in Mathematics156, Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  12. Hartshorne, R.: Ample vector bundles. Inst. Hautes Études Sci. Publ. Math. 55–94 (1966)

  13. Howard, A., Smyth, B.: Kähler surfaces of nonnegative curvature. J. Differential Geometry5, 491–502 (1971)

    Google Scholar 

  14. Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  15. Kobayashi, S., Nomizu, K.: Foundations of differential geometry. In: Interscience Tracts I (1963), and II (1968), New York: Wiley

    Google Scholar 

  16. Kobayashi, S., Ochiai, T.: On complex manifolds with positive tangent bundles. J. Math. Soc. Japan22, 499–525 (1970)

    Google Scholar 

  17. Kodaira, K.: On the structure of compact complex analytic surfaces, I, II, III, IV. Amer. J. Math.86, 751–798 (1964);88, 687–721 (1966);90, 55–83 (1968);90, 1048–1066 (1968)

    Google Scholar 

  18. Kodaira, K.: On Kähler varieties of restricted type. Ann. Math.60, 28–48 (1954)

    Google Scholar 

  19. Lichnerowicz, A.: Sur les transformations analytiques d'une variete Kähleriene compacte. Colloque Geom. Diff. Global, Bruxelles, pp. 11–26, 1958

  20. Matsushima, Y.: Hodge manifolds with zero first Chern class. J. Differential Geometry3, 477–489 (1969)

    Google Scholar 

  21. Matsushima, Y.: Sur les espaces homogenes complexes. Nagoya Math. J.18, 1–12 (1961)

    Google Scholar 

  22. Morrow, J., Kodaira, K.: Complex Manifolds. New York: Holt, Reinhart & Winston 1971

    Google Scholar 

  23. Moore, J.D.: Isometric immersions of Riemannian products. J. Differential Geometry5, 159–168 (1971)

    Google Scholar 

  24. Nagano, T.: Homogeneous sphere bundles and the isotropic Riemannian manifolds. Nagoya Math. J.15, 29–55 (1959)

    Google Scholar 

  25. Suwa, T.: On ruled surfaces of genus 1. J. Math. Soc. Japan2, 258–291 (1969)

    Google Scholar 

  26. Van de Ven, A.: On holomorphic fields of complex line elements with isolated singularities. Ann. Inst. Fourier (Grenoble)14, 99–130 (1964)

    Google Scholar 

  27. Wang, H.C.: Closed manifolds with homogeneous complex structure. Amer. J. Math.76, 1–32 (1954)

    Google Scholar 

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This work partially supported by National Science Foundation Grant GP 32460.

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Yau, ST. On the curvature of compact Hermitian manifolds. Invent Math 25, 213–239 (1974). https://doi.org/10.1007/BF01389728

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