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Proceedings of the American Mathematical Society

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Families of negatively curved Hermitian manifolds


Author: Michael J. Cowen
Journal: Proc. Amer. Math. Soc. 39 (1973), 362-366
MSC: Primary 32L05; Secondary 32H25, 53C55
DOI: https://doi.org/10.1090/S0002-9939-1973-0315163-X
MathSciNet review: 0315163
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Abstract: A complex analytic family of compact hermitian manifolds has negative holomorphic sectional curvature in a neighborhood of any fibre having negative holomorphic sectional curvature.


References [Enhancements On Off] (What's this?)

  • [1] H. Grauert and H. Reckziegel, Hermitesche Metriken und normale Familien holomorpher Abbildungen, Math. Z. 89 (1965), 108-125. MR 33 #2827. MR 0194617 (33:2827)
  • [2] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., no. 2, Marcel Dekker, New York, 1970. MR 43 #3503. MR 0277770 (43:3503)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315163-X
Keywords: Holomorphic sectional curvature, hyperbolic manifold, analytic family, differential metric
Article copyright: © Copyright 1973 American Mathematical Society

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