Skip to main content

Premières formes de Chern des variétés kählériennes compactes [d’après E. Calabi, T. Aubin et S. T. Yau]

Part of the Lecture Notes in Mathematics book series (LNM,volume 710)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. M. APTE-Sur certaines classes caractéristiques des variétés kählériennes compactes, C.R.Acad. Sci. Paris, 240 (1955), 149–151.

    MATH  MathSciNet  Google Scholar 

  2. M. ATIYAH, N. HITCHIN, I. M. SINGER-Deformations of instantons, Proc. Nat. Acad. Sci. U.S.A., 74 (1977), 2662–2663.

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. T. AUBIN-Métriques riemanniennes et courbure, J. Diff. Geom., 4 (1970), 383–424.

    MATH  MathSciNet  Google Scholar 

  4. T. AUBIN-Equations du type de Monge-Ampère sur les variétés kählériennes compactes, C.R. Acad. Sci. Paris, 283 (1976), 119–121.

    MATH  MathSciNet  Google Scholar 

  5. M. BERGER-Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. France, 83 (1955), 279–330.

    MATH  Google Scholar 

  6. M. BERGER, A. LASCOUX-Variétés kählériennes compactes, Lecture Notes in Math vol. 154, Springer, 1970.

    Google Scholar 

  7. S. BOCHNER-Vector fields and Ricci curvature, Bull. A. M. S., 52 (1946), 776–797.

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. J.-P. BOURGUIGNON-Sur les géodésiques fermées des variétés quaternioniennes de dimension 4, Math. Ann., 221 (1976), 153–165.

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. E. CALABI-The space of Kähler metrics, Proc. Internat. Congress Math. Amsterdam, vol. 2 (1954), 206–207.

    Google Scholar 

  10. E. CALABI-On Kähler manifolds with vanishing canonical class, Algebraic Geometry and Topology, A Symposium in honor of S. Lefschetz, Princeton Univ. Press, (1955), 78–89.

    Google Scholar 

  11. E. CALABI-Improper affine hyperspheres and a generalization of a theorem of K. Jörgens, Mich. Math. J., 5 (1958), 105–126.

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. S. S. CHERN-Characteristic classes of Hermitian manifolds, Ann. of Math., 47 (1946), 85–121.

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. H. GUGGENHEIMER-Über vierdimensionale Einsteinraüme, Experientia 8, (1952), 420–421.

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. F. HIRZEBRUCH-Some problems on differentiable and complex manifolds, Ann. Math., 60 (1954), 210–236.

    CrossRef  MathSciNet  Google Scholar 

  15. F. HIRZEBRUCH-Topological methods in algebraic geometry, Grundlehren der math. Wiss., Springer, Berlin-Heidelberg-New York, 1966.

    MATH  Google Scholar 

  16. F. HIRZEBRUCH, K. KODAIRA-On the complex projective spaces, J. Math. Pures appl., 36 (1957), 201–216.

    MATH  MathSciNet  Google Scholar 

  17. N. HITCHIN-Compact four-dimensional Einstein manifolds, J. Diff. Geom., 9(1974), 435–441.

    MATH  MathSciNet  Google Scholar 

  18. S. KOBAYASHI, T. OCHIAI-On compact Kähler manifolds with positive holomorphic bisectional curvature, Proc. Symp. Pure Maths. A.M.S., XXVII, Part 2, Stanford, (1975), 113–123.

    Google Scholar 

  19. K. KODAIRA-Collected works, Princeton Univ. Press, Princeton, vol. III, 1975.

    Google Scholar 

  20. A. LICHNEROWICZ-Spineurs harmoniques, note aux C.R. Acad. Sci. Paris, 257 (1963), 7–9.

    MATH  MathSciNet  Google Scholar 

  21. Y. MATSUSHIMA-Remarks on Kähler-Einstein manifolds, Nagoya Math. J., 46 (1972), 161–173.

    MATH  MathSciNet  Google Scholar 

  22. C. MORREY-Multiple integrals in the calculus of variations, Grundlehren der mathematischen Wiss., Springer, 1966.

    Google Scholar 

  23. L. NIRENBERG-Monge-Ampère equations and some associated problems in geometry, Proc. Int. Cong. Vancouver, Tome II (1974), 275–279.

    Google Scholar 

  24. A. POLOMBO-Nombres caractéristiques d’une surface kählérienne, Note aux C.R. Acad. Sci. Paris, 283 (1976), 1025–1028.

    MATH  MathSciNet  Google Scholar 

  25. G. de RHAM-Variétés différentiables, Paris, Hermann, 1960.

    MATH  Google Scholar 

  26. F. SEVERI-Some remarks on the topological characterization of algebraic surfaces, in Studies presented to R. von Mises (1954), Academic Press, New York, 54–61.

    Google Scholar 

  27. A. VAN DE VEN-Some recent results on surfaces of general type, Séminaire Bourbaki, Exposé 500, fév. 1977, Lecture Notes in Math., no 677, Springer, 155–166.

    Google Scholar 

  28. S. T. YAU-On the curvature of compact Hermitian manifolds, Inventiones Math., 25 (1974), 213–239.

    CrossRef  MATH  Google Scholar 

  29. S. T. YAU-On Calabi’s conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A., 74 (1977), 1798–1799.

    CrossRef  MATH  MathSciNet  Google Scholar 

  30. S. T. YAU-On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I, Preprint, 1977.

    Google Scholar 

  31. S. T. YAU, S. Y. CHENG-On the regularity of the Monge-Ampère equation \(\det \left( {\frac{{\partial ^2 u}}{{\partial x^i \partial x^j }}} \right) = F(x,u)\), Comm. Pure Appl. Math., XXX (1977), 47–68.

    MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 N. Bourbaki

About this paper

Cite this paper

Bourguignon, JP. (1979). Premières formes de Chern des variétés kählériennes compactes [d’après E. Calabi, T. Aubin et S. T. Yau]. In: Séminaire Bourbaki vol. 1977/78 Exposés 507–524. Lecture Notes in Mathematics, vol 710. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0069970

Download citation

  • DOI: https://doi.org/10.1007/BFb0069970

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09243-8

  • Online ISBN: 978-3-540-35340-9

  • eBook Packages: Springer Book Archive