Abstract
We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ℂn, intersections of complex-ellipsoidal domains in ℂ2, and intersections of fractional linear transforms of the unit ball in ℂ2. In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ℂ2, the sum of the Bergman metrics is a Kähler metric with negative curvature operator.
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Work of the second author was partially supported by the National Science Foundation.
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Cheung, CK., Wu, H. Some new domains with complete Kähler metrics of negative curvature. J Geom Anal 2, 37–78 (1992). https://doi.org/10.1007/BF02921334
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DOI: https://doi.org/10.1007/BF02921334