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Ricci-flat Kähler metrics on affine algebraic manifolds

Part of the Lecture Notes in Mathematics book series (LNM,volume 1339)

Keywords

  • Line Bundle
  • Sobolev Inequality
  • Chern Class
  • Ricci Curvature
  • Noncompact Manifold

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References

  1. T. Aubin, Nonlinear analysis on manifolds, Monge-Ampère equations, Springer-Verlag, Berlin/New York, 1982.

    CrossRef  MATH  Google Scholar 

  2. —, Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la demonstration d'une inégalité, J. Funct. Anal., 57 (1984), 143–153.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. S. Bando and T. Mabuchi, Uniqueness of Einstein Kähler metrics modulo connected group actions, in "Algebraic Geometry, Sendai, 1985", ed. T. Oda, Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo, and North-Holland, Amsterdam, 1987, 11–40.

    Google Scholar 

  4. J. P. Bourguignon et al., Première classe de Chern et courbure de Ricci: preuve de la conjecture de Calabi, Astérisque 58, Soc. Math. France, 1978.

    Google Scholar 

  5. E. Calabi, Métriques Kählériennes et fibrés holomorphes, Ann. Sci. Ec. Norm. Sup. Paris, 4me Sér. 12 (1979), 269–294.

    MathSciNet  MATH  Google Scholar 

  6. —, Isometric families of Kähler structures, in "Chern Sump. 1979", ed. W.-Y. Hsiang et al., Springer-Verlag, Berlin/New York, 1980, 23–39.

    CrossRef  Google Scholar 

  7. —, Extremal Kähler metrics, in "Seminar on Differential Geometry", ed. S.-T. Yau, Princeton Univ. Press, Ann. Math. Stud., 102 (1982), 259–290.

    Google Scholar 

  8. S.-Y. Cheng and S.-T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math., 28 (1975), 333–354.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. —, On the existence of a complete Kähler-Einstein metric on noncompact complex manifolds and regularity of Fefferman's equation, Comm. Pure Appl. Math., 32 (1980), 507–544.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin/New York, 1983.

    CrossRef  MATH  Google Scholar 

  11. N. J. Hitchin, Polygons and gravitons, Math. Proc. Camb. Phil. Soc., 83 (1979), 465–476.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. N. J. Hitchin, A. Karlehede, U. Lindstrom, and M. Rocek, Hyperkähler metrics and supersymmetry, Comm. Math. Phys., 108 (1987), 535–589.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. M. Itoh, Quaternion structure on the moduli space of Yang-Mills connections, Math. Ann., 276 (1987), 581–593.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. R. Kobayashi, Einstein-Kähler V-metrics on open Satake V-surfaces with isolated quatient singulkarities, Math. Ann., 272 (1985), 385–398.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. S. Kobayashi, On compact Kähler manifolds with positive definite Ricci tensor, Ann. Math., 7 (1961), 570–574.

    CrossRef  MATH  Google Scholar 

  16. —, Simple vector bundles over symplectic Kähler manifolds, Proc. Japan Acad., 62, Ser. A, (1986), 21–24.

    CrossRef  MATH  Google Scholar 

  17. P. B. Kronheimer, ALE gravitational instantons, thesis, Oxford Univ., (1986).

    Google Scholar 

  18. —, Instantons gravitationals et singularités de Klein, C. R. Acad. Sci. Paris, 303, Ser. I, (1986), 53–55.

    MathSciNet  MATH  Google Scholar 

  19. J. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., New York, 1971.

    MATH  Google Scholar 

  20. A. Nadel and H. Tsuji, Compactification of complete Kähler manifolds of negative Ricci curvature, (preprint, Harvard Univ. and Tokyo Metropolitan Univ.).

    Google Scholar 

  21. Y.-T. Siu, The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and finite symmetry group, (preprint, Harvard Univ.).

    Google Scholar 

  22. G. Tian, On Kähler-Einstein metrics on certain Kähler manifolds with c1(M)>0, Invent. Math., 89 (1987), 225–246.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. G. Tian and S.-T. Yau, Kähler-Einstein metrics on complex surfaces with c1>0, Comm. Math. Phys., 112 (1987), 175–203.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. H. Tsuji, Complete negatively pinched Kähler surfaces of finite volume, (preprint, Harvard Univ. and Tokyo Metropolitan Univ.).

    Google Scholar 

  25. S.-T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28 (1975), 201–228.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. —, On the Ricci curvature of a compact Kähler manifold and complex Monge-Ampère equation, I, Comm. Pure Appl. Math., 31 (1978), 339–411.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. —, A general Schwarz lemma for Kähler manifolds, Amer. J. Math., 100 (1978), 197–203.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. —, Nonlinear analysis in geometry, L'Enseig. Math., 33 (1987), 109–158.

    MathSciNet  MATH  Google Scholar 

  29. J. Cerf, Topologie de certains espaces de plongements, Bull. Soc. math. France, 89 (1961), 227–380.

    MathSciNet  MATH  Google Scholar 

  30. H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331–368.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Dedicated to Professor Ichiro Satake on his 60th Birthday

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© 1988 Springer-Verlag

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Bano, S., Kobayashi, R. (1988). Ricci-flat Kähler metrics on affine algebraic manifolds. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083044

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  • DOI: https://doi.org/10.1007/BFb0083044

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