Locally homogeneous complex manifolds

  title={Locally homogeneous complex manifolds},
  author={Phillip A. Griffiths and Wilfried Schmid},
  journal={Acta Mathematica},
In this paper we discuss some geometric and analytic properties of a class of locally homogeneous complex manifolds. Our original motivation came from algebraic geometry where certain non-compact, homogeneous complex manifolds arose natural ly from the period matrices of general algebraic varieties in a similar fashion to the appearance of the Siegel upper-half-space from the periods of algebraic curves. However, these manifolds arc generally not Hermit ian symmetric domains and, because of… Expand
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Homogeneous complex manifolds and representations of semisimple lie groups.
  • W. Schmid
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1968
The generalized Borel-Weil theorem and Theorem 1 are proved, which show that the structure of a holomorphic line bundle such that the action of G on D lifts to the sheaf of germs of holomorphic sections of Lx, O(L,) is an infinite-dimensional Frechet space on which G acts continuously. Expand
Some results on locally homogeneous complex manifolds.
  • P. Griffiths
  • Physics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1966
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© Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
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