Inventiones mathematicae

, Volume 160, Issue 3, pp 501–525 | Cite as

A negatively curved Kähler threefold not covered by the ball

  • Martin DerauxEmail author


We construct examples of three-dimensional compact Kähler manifolds with negative curvature, not covered by the ball. Our manifolds are obtained as a natural generalization of the two-dimensional examples discovered by Mostow and Siu, using their description in terms of monodromy covers of hypergeometric functions. Each example is obtained from a hypergeometric monodromy group in PU(3,1) that is not discrete but has finite local monodromy. We describe a manifold on which the group acts discretely, and check that it has a compact quotient with the above features. The examples are locally described as branched covers of the ball, with totally geodesic branch locus.


Manifold Hypergeometric Function Natural Generalization Negative Curvature Branch Locus 
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© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Centre de MathématiquesEcole PolytechniquePalaiseauFrance

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