Acta Mathematica

, 123:253 | Cite as

Locally homogeneous complex manifolds

  • Phillip Griffiths
  • Wilfried Schmid
Article

Keywords

Manifold Complex Manifold Homogeneous Complex Homogeneous Complex Manifold 

References

  1. [1].
    Andreotti, A. &Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes.Bull. Soc. Math. France, 90 (1962), 193–259.MathSciNetMATHGoogle Scholar
  2. [2].
    Andreotti, A. &Vesentini, E., Carleman estimates for the Laplace-Beltrami operator on complex manifolds.Inst. Hautes Études Sci. Publ. Math., 25 (1965), 81–130.MathSciNetGoogle Scholar
  3. [3].
    Atiyah, M. F. &Singer, I. M., The index of elliptic operators I, III.Ann. of Math., 87 (1968), 484–530, and 546–604.CrossRefMathSciNetGoogle Scholar
  4. [4].
    Borel, A., Kählerian coset spaces of semi-simple Lie groups.Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1140–1151.MathSciNetGoogle Scholar
  5. [5].
    Borel, A. & Weil, A., Representations linéaires et espaces homogènes kähleriennes des groupes de Lie compacts.Séminaire Bourbaki, (May 1954) exp. 100.Google Scholar
  6. [6].
    Borel, A. &Hirzebruch, F., Characteristic classes and homogeneous spaces I, II.Amer. J. Math., 80 (1958), 458–438 and 81 (1959), 315–382.MathSciNetGoogle Scholar
  7. [7].
    Bott, R., Homogeneous vector bundles.Ann. of Math., 66 (1957), 203–248.CrossRefMATHMathSciNetGoogle Scholar
  8. [8].
    Calabi, E. &Vesentini, E., On compact, locally symmetric Kähler manifolds.Ann. of Math., 71, (1960), 472–507.CrossRefMathSciNetGoogle Scholar
  9. [9].
    Grauert, H. &Reckziegel, H., Hermitesche Metriken und normale Familien holomopher Abbildungen.Math. Z., 89 (1965), 108–125.CrossRefMathSciNetMATHGoogle Scholar
  10. [10].
    Griffiths, P. A., Some results on locally homogeneous complex, manifolds.Proc. Nat. Acad. Sci. U.S.A., 56 (1966), 413–416.MATHMathSciNetGoogle Scholar
  11. [11].
    —, Periods of integrals on algebraic manifolds I, II.Amer. J. Math., 90 (1968), 568–626.MATHMathSciNetGoogle Scholar
  12. [12].
    Griffiths, P. A., Periods of integrals on algebraic manifolds III. To appear.Google Scholar
  13. [13].
    Griffiths, P. A., Hermitian differential geometry and positive vector bundles. To appear.Google Scholar
  14. [14].
    Harish-Chandra, Discrete series for semisimple Lie groups II.Acta Math., 116 (1966), 1–111.CrossRefMathSciNetMATHGoogle Scholar
  15. [15].
    Helgason, S.,Differential geometry and symmetric spaces. Academic Press, New York 1962.MATHGoogle Scholar
  16. [16].
    Hirzebruch, F.,Neue topologische Methoden in der algebraischen Geometrie. Ergebnisse der Mathematik, 9 (1956).Google Scholar
  17. [17].
    Hirzebruch, F., Automorphe Formen und der Satz von Reimann-Roch.Symposium International de Topologica Algebraica, Universidad de Mexico (1958), 129–143.Google Scholar
  18. [18].
    Hodge, W. V. D.,The theory and applications of harmonic integrals. 2nd ed., Cambridge University Press (1959).Google Scholar
  19. [19].
    Ise, M., Generalized automorphic forms and certain holomorphic vector bundles.Amer. J. Math., 86 (1964), 70–108.MATHMathSciNetGoogle Scholar
  20. [20].
    Kobayashi, S., Invariant distances on complex manifolds, and holomorphic mappings.J. Math. Soc. Japan, 19 (1967), 460–480.MATHMathSciNetCrossRefGoogle Scholar
  21. [21].
    Kostant, B., Lie algebra cohomology and the generalized Borel-Weil theorem.Ann. of Math., 74 (1961), 329–387.CrossRefMATHMathSciNetGoogle Scholar
  22. [22].
    Kwack, M. H.,Generalizations of the big Picard theorem. Thesis, Berkeley, 1968.Google Scholar
  23. [23].
    Langlands, R., The dimensions of spaces of automorphic forms.Amer. J. Math. 85 (1963), 99–125.MATHMathSciNetGoogle Scholar
  24. [24].
    —, Dimensions of spaces of automorphic forms. Algebraic groups and discontinuous subgroups.Proc. of Symposia in Pure Mathematics, vol. IX, Amer. Math. Soc., Providence, R. I (1966), 253–257.Google Scholar
  25. [25].
    Matsushima, Y. &Murakami, S., On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds.Ann. of Math., 78 (1963), 365–416.CrossRefMathSciNetGoogle Scholar
  26. [26].
    — On certain cohomology groups attached to Hermitian symmetric spaces.Osaka J. Math., 2 (1965), 1–35.MATHMathSciNetGoogle Scholar
  27. [27].
    Okamoto, K. &Ozeki, H., On square-integrable\(\bar \partial\) spaces attached to Hermitian symmetric spaces.Osaka J. Math., 4 (1967), 95–110.MathSciNetMATHGoogle Scholar
  28. [28].
    Schmid, W.,Homogeneous complex manifolds and representations of semisimple Lie groups. Thesis, Berkeley, 1967.Google Scholar
  29. [29].
    —, Homogeneous complex manifolds and representations of semisimple Lie groups.Proc. Nat. Acad. Sci. U.S.A., 59 (1968), 56–59.MATHMathSciNetGoogle Scholar
  30. [30].
    Stiefel, E., Kristallographische Bestimmung der Charactere der geschlossenen Lie'schen Gruppen.Comm. Math. Helv., 17 (1944), 165–200.MathSciNetGoogle Scholar
  31. [31].
    Wang, H. C., Closed manifolds with homogeneous complex structure.Amer. J. Math., 76 (1954), 1–32.MATHMathSciNetGoogle Scholar
  32. [32].
    Wu, H. H., Normal families of holomorphic mappings.Acta Math., 119 (1967), 193–233.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1969

Authors and Affiliations

  • Phillip Griffiths
    • 1
    • 2
  • Wilfried Schmid
    • 1
    • 2
  1. 1.Princeton UniversityPrinceton
  2. 2.Columbia UniversityNew York

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