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Threefolds with holomorphic normal projective connections

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References

  1. Atiyah, M.F.: Complex Analytic Connections in Fibre Bundles. Trans. of AMS 85, 181–207 (1957)

    MathSciNet  MATH  Google Scholar 

  2. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self–duality in four–dimensional Riemannian geometry. Proc. R. Soc. Lon. A. 362, 425–461 (1978)

    MathSciNet  MATH  Google Scholar 

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

  4. Beauville, A.: Variétés Kählériennes dont la premiere classe de Chern est nulle. J. Diff. Geom. 18, 755–782 (1983)

    MATH  Google Scholar 

  5. Campana, F.: Réduction d’Albanese d’un morphisme propre et faiblement Kählérien I. Comp. Math. 54, 373–398 (1985)

    MathSciNet  MATH  Google Scholar 

  6. Cartan, E.: Sur les variétés à connexion projective. Bull. de la Soc. Math. de France 52, 205–241 (1924)

    MATH  Google Scholar 

  7. Demailly, J.–P., Peternell, Th., Schneider, M.: Compact complex manifolds with nef tangent bundles. J. Alg. Geom. 3, 295–345 (1994)

    MathSciNet  MATH  Google Scholar 

  8. Faltings, G., Chai, C.–L.: Degeneration of Abelian Varieties. Springer 1990

  9. Fujiki, A.: On the structure of compact complex manifolds in . E. Adv. Stud. Pure Math. 1, 231–302 (1983)

    Google Scholar 

  10. Griffiths, P.A.: Periods of integrals on algebraic manifolds, III. Publ. IHES 38, 125–180 (1970)

    MATH  Google Scholar 

  11. Gunning, R.: On Uniformizations of Complex Manifolds. Mathematical Notes 22, Princeton Univ. Press 1978

  12. Hitchin, N.J.: Kählerian twistor spaces. Proc. London Math. Soc. 43, 133–150 (1981)

    MathSciNet  MATH  Google Scholar 

  13. Hwang, J.–M., Mok, N.: Uniruled projective manifolds with irreducible reductive G–structures. J. reine angew. Math. 490, 55–64 (1997)

    MathSciNet  MATH  Google Scholar 

  14. Inoue, M., Kobayashi, S., Ochiai, T.: Holomorphic affine connections on compact complex surfaces. J. Fac. Sci., Tokyo, Sect. I A 27, 247–264 (1980)

    Google Scholar 

  15. Kawamata, Y.: Abundance theorem for minimal threefolds. Inv. Math. 108, 229–246 (1992)

    MathSciNet  MATH  Google Scholar 

  16. Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. Adv. Stud. Pure Math. 10, 283–360 (1987)

    MATH  Google Scholar 

  17. Kobayashi, S., Ochiai, T.: Holomorphic projective structures on compact complex surfaces I, II. Math. Ann. 249, 75–94 (1980); 255, 519–521 (1981)

    MathSciNet  MATH  Google Scholar 

  18. Kobayashi, S., Ochiai, T.: Holomorphic structures modeled after compact Hermitian symmetric spaces. Manifolds and Lie groups, Pap. in Honor of Y. Matsushima, Prog. Math. 14, 207–222 (1981)

    Google Scholar 

  19. Kobayashi, S., Wu, H.: Complex differential geometry. DMV Sem. 3 (1983)

  20. Kodaira, K.: On compact Analytic Surfaces: II. Ann. Math. 77, 563–626 (1963)

    MATH  Google Scholar 

  21. Lange, H., Birkenhake, C.: Complex Abelian Varieties. Springer 1992

  22. Miyaoka, Y., Peternell, T.: Geometry of Higher Dimensional Algebraic Varieties. DMV Sem. 26 (1997)

  23. Molzon, R., Mortensen, K.: The Schwarzian derivative for maps between manifolds with complex projective connections. Tr. AMS 348, 3015–3036 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mori, S.: Projective manifolds with ample tangent bundles. Ann. Math. 110, 593–606 (1979)

    MathSciNet  MATH  Google Scholar 

  25. Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math. 116, 133–176 (1982)

    MathSciNet  MATH  Google Scholar 

  26. Mori, S., Mukai, S.: The uniruledness of the moduli space of curves of genus 11. Alg. Geom., Proc. Tokyo/Kyoto 1982, LNM 1016, 334–353 (1983)

  27. Oguiso, K.: On algebraic fiber space structures on a Calabi–Yau 3–fold. Int. J. of Math. 4, 439–465 (1993)

    MathSciNet  MATH  Google Scholar 

  28. Peternell, T.: Manifolds of Semi–positive Curvature. Cetraro 1994, Springer LNM 1646, 98–142 (1996)

  29. Peters, C.: Arakelov–type inequalities for Hodge bundles. Preprint (2000)

  30. Salamon, S.: Quaternionic Kähler manifolds. Inv. Math. 67, 143–171 (1982)

    MathSciNet  MATH  Google Scholar 

  31. Satake, I.: Algebraic structures of symmetric domains. Princeton University Press 1980

  32. Tian, G.: Kähler–Einstein Metrics on Algebraic Manifolds. Cetraro 1994, Springer LNM 1646, 143–185 (1996)

  33. Viehweg, E., Zuo, K.: On the isotriviality of families of projective manifolds over curves. J. Alg. Geom. 10, 781–799 (2001)

    MathSciNet  MATH  Google Scholar 

  34. Viehweg, E., Zuo, K.: A characterization of certain Shimura curves in the moduli stack of abelian varieties. Preprint (2002)

  35. Van de Ven, A.: A property of algebraic varieties in complex projective spaces. Colloque de géom. diff. gl. (Bruxelles, 1958)

  36. Ye, Y.G.: On Fano manifolds with normal projective connections. Int. J. Math. 5, 265–271 (1994)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bayreuth, D–95440, Bayreuth, Germany

    Priska Jahnke & Ivo Radloff

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  1. Priska Jahnke
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  2. Ivo Radloff
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Correspondence to Priska Jahnke.

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The authors were supported by a Forschungsstipendium of the Deutsche Forschungsgemeinschaft and the DFG–Schwerpunkt Globale Methoden in der komplexen Geometrie.

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Jahnke, P., Radloff, I. Threefolds with holomorphic normal projective connections. Math. Ann. 329, 379–400 (2004). https://doi.org/10.1007/s00208-004-0406-8

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