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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Compact manifolds in hyperbolicity

Author: Robert Brody
Journal: Trans. Amer. Math. Soc. 235 (1978), 213-219
MSC: Primary 32H20
MathSciNet review: 0470252
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Abstract: In this paper we establish the strongest possible criterion for the hyperbolicity of a compact complex manifold: such a manifold is hyperbolic if and only if it contains no (nontrivial) complex lines. In addition, we study the behavior of such manifolds under deformation and, in particular, answer the two most natural questions about such deformations: Is the space of hyperbolic complex structures on a given ${C^\infty }$ manifold open in the space of all its complex structures? (Yes.) Is it closed? (Not in general.) These results answer questions first posed by Kobayashi in [4] and [5].

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

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Article copyright: © Copyright 1978 American Mathematical Society