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On holomorphic connections

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Part of the Lecture Notes in Mathematics book series (LNM,volume 838)

Keywords

  • Chern Class
  • Betti Number
  • Elliptic Surface
  • Affine Connection
  • Compact Complex Manifold

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Footnotes and References

  1. Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades, Crelle J. 70 (1869), 46–70. Christoffel’s original symbol {jk i} is now commonly denoted by Γ ijk or {i jk}.

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  2. M. Inoue-S. Kobayashi-T. Ochiai, Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. Univ. Tokyo (1980), to appear.

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  3. S. Kobayashi-T. Ochiai, Holomorphic projective structures on compact complex surfaces, to appear.

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  4. R. Gunning, On Uniformization of Complex Manifolds; The Role of Connections, Math. Notes No. 22, 1978, Princeton Univ. Press.

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  5. In this section, the Chern classes ci are considered as elements of H*(M;R) (rather than elements of H*(M;Z)).

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  6. pp.73–74 of A. Lascoux-M. Berger, Variétés Kählériennes Compactes, Lecture Notes in Math. No. 154 (1970), Springer-Verlag.

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  7. S. T. Yau, Calabi’s conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. USA 74 (1977), 1798–1799.

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  8. K. Kodaira, Pluricanonical systems on algebraic surfaces of general type, J. Math. Soc. Japan 20 (1968), 170–192.

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  9. K. Kodaira, On compact complex analytic surfaces II, Ann. Math. 77 (1963), 563–626; III 78 (1963), 1–40.

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  10. K. Maehara, On elliptic surfaces whose first Betti numbers are odd, Intl. Symp. Alg. Geometry, Kyoto, 1977, 565–574.

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  11. For Hopf surfaces, see K. Kodaira, On the structure of compact complex analytic surfaces II, Amer. J. Math. 88 (1966), 682–721.

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  12. See Note 7).

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  13. M. Inoue, On surfaces of class VII0, Inventiones Math. 24 (1974), 269–310.

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  14. F. A. Bogomolov, Classification of surfaces of class VII0 with b2=0, Math. USSR Izvestija 10 (1976), 255–269. See also the review of this paper by M. Reid in Math. Reviews, vol. 55, #359.

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  15. A. Fischer-J. A. Wolf, The structure of compact Ricci-flat Riemannian manifolds, J. Diff. Geometry 10 (1975), 277–288.

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© 1981 Springer-Verlag

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Kobayashi, S. (1981). On holomorphic connections. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088853

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  • DOI: https://doi.org/10.1007/BFb0088853

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10285-4

  • Online ISBN: 978-3-540-38419-9

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