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Locally homogeneous complex manifolds

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Acta Mathematica

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References

  1. Andreotti, A. &Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes.Bull. Soc. Math. France, 90 (1962), 193–259.

    MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  3. Atiyah, M. F. &Singer, I. M., The index of elliptic operators I, III.Ann. of Math., 87 (1968), 484–530, and 546–604.

    Article  MathSciNet  Google Scholar 

  4. Borel, A., Kählerian coset spaces of semi-simple Lie groups.Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1140–1151.

    MathSciNet  Google Scholar 

  5. Borel, A. & Weil, A., Representations linéaires et espaces homogènes kähleriennes des groupes de Lie compacts.Séminaire Bourbaki, (May 1954) exp. 100.

  6. Borel, A. &Hirzebruch, F., Characteristic classes and homogeneous spaces I, II.Amer. J. Math., 80 (1958), 458–438 and 81 (1959), 315–382.

    MathSciNet  Google Scholar 

  7. Bott, R., Homogeneous vector bundles.Ann. of Math., 66 (1957), 203–248.

    Article  MATH  MathSciNet  Google Scholar 

  8. Calabi, E. &Vesentini, E., On compact, locally symmetric Kähler manifolds.Ann. of Math., 71, (1960), 472–507.

    Article  MathSciNet  Google Scholar 

  9. Grauert, H. &Reckziegel, H., Hermitesche Metriken und normale Familien holomopher Abbildungen.Math. Z., 89 (1965), 108–125.

    Article  MathSciNet  MATH  Google Scholar 

  10. Griffiths, P. A., Some results on locally homogeneous complex, manifolds.Proc. Nat. Acad. Sci. U.S.A., 56 (1966), 413–416.

    MATH  MathSciNet  Google Scholar 

  11. —, Periods of integrals on algebraic manifolds I, II.Amer. J. Math., 90 (1968), 568–626.

    MATH  MathSciNet  Google Scholar 

  12. Griffiths, P. A., Periods of integrals on algebraic manifolds III. To appear.

  13. Griffiths, P. A., Hermitian differential geometry and positive vector bundles. To appear.

  14. Harish-Chandra, Discrete series for semisimple Lie groups II.Acta Math., 116 (1966), 1–111.

    Article  MathSciNet  MATH  Google Scholar 

  15. Helgason, S.,Differential geometry and symmetric spaces. Academic Press, New York 1962.

    MATH  Google Scholar 

  16. Hirzebruch, F.,Neue topologische Methoden in der algebraischen Geometrie. Ergebnisse der Mathematik, 9 (1956).

  17. Hirzebruch, F., Automorphe Formen und der Satz von Reimann-Roch.Symposium International de Topologica Algebraica, Universidad de Mexico (1958), 129–143.

  18. Hodge, W. V. D.,The theory and applications of harmonic integrals. 2nd ed., Cambridge University Press (1959).

  19. Ise, M., Generalized automorphic forms and certain holomorphic vector bundles.Amer. J. Math., 86 (1964), 70–108.

    MATH  MathSciNet  Google Scholar 

  20. Kobayashi, S., Invariant distances on complex manifolds, and holomorphic mappings.J. Math. Soc. Japan, 19 (1967), 460–480.

    Article  MATH  MathSciNet  Google Scholar 

  21. Kostant, B., Lie algebra cohomology and the generalized Borel-Weil theorem.Ann. of Math., 74 (1961), 329–387.

    Article  MATH  MathSciNet  Google Scholar 

  22. Kwack, M. H.,Generalizations of the big Picard theorem. Thesis, Berkeley, 1968.

  23. Langlands, R., The dimensions of spaces of automorphic forms.Amer. J. Math. 85 (1963), 99–125.

    MATH  MathSciNet  Google Scholar 

  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. Matsushima, Y. &Murakami, S., On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds.Ann. of Math., 78 (1963), 365–416.

    Article  MathSciNet  Google Scholar 

  26. — On certain cohomology groups attached to Hermitian symmetric spaces.Osaka J. Math., 2 (1965), 1–35.

    MATH  MathSciNet  Google Scholar 

  27. Okamoto, K. &Ozeki, H., On square-integrable\(\bar \partial\) spaces attached to Hermitian symmetric spaces.Osaka J. Math., 4 (1967), 95–110.

    MathSciNet  MATH  Google Scholar 

  28. Schmid, W.,Homogeneous complex manifolds and representations of semisimple Lie groups. Thesis, Berkeley, 1967.

  29. —, Homogeneous complex manifolds and representations of semisimple Lie groups.Proc. Nat. Acad. Sci. U.S.A., 59 (1968), 56–59.

    MATH  MathSciNet  Google Scholar 

  30. Stiefel, E., Kristallographische Bestimmung der Charactere der geschlossenen Lie'schen Gruppen.Comm. Math. Helv., 17 (1944), 165–200.

    MathSciNet  Google Scholar 

  31. Wang, H. C., Closed manifolds with homogeneous complex structure.Amer. J. Math., 76 (1954), 1–32.

    MATH  MathSciNet  Google Scholar 

  32. Wu, H. H., Normal families of holomorphic mappings.Acta Math., 119 (1967), 193–233.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Princeton University, Princeton, N.J.

    Phillip Griffiths & Wilfried Schmid

  2. Columbia University, New York, N.Y.

    Phillip Griffiths & Wilfried Schmid

Authors
  1. Phillip Griffiths
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  2. Wilfried Schmid
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Additional information

During the preparation of this paper, the first named author was partially supported by NSF grant GP-7952X at the Institute for Advanced Study, and the second named author by NSF grant GP-8008 at the University of California, Berkeley.

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Griffiths, P., Schmid, W. Locally homogeneous complex manifolds. Acta Math. 123, 253–302 (1969). https://doi.org/10.1007/BF02392390

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