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Ricci curvature and holomorphic convexity in Kähler manifolds


Author: Karen R. Pinney
Journal: Proc. Amer. Math. Soc. 121 (1994), 1211-1216
MSC: Primary 32L07; Secondary 32C17, 53C55
DOI: https://doi.org/10.1090/S0002-9939-1994-1189751-9
MathSciNet review: 1189751
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Abstract: In this paper we show that if a smoothly bounded, relatively compact domain in a complex manifold admits a complete Kähler metric with certain bounds on its Ricci tensor, then the domain must be holomorphically convex. This gives an obstruction for the existence of a complete Kähler-Einstein metric on such domains.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1189751-9
Article copyright: © Copyright 1994 American Mathematical Society

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