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arXiv · 1101.0186

Kähler-Einstein metrics on strictly pseudoconvex domains

Craig van Coevering
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Abstract

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete Kähler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on $\partial M$ is normal. In this case M must be a domain in a resolution of the Sasaki cone over $\partial M$. We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a Kähler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities. Many examples are given of Kähler-Einstein strictly pseudoconvex manifolds on bundles and resolutions.

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Craig van Coevering. 2011-01-20. Kähler-Einstein metrics on strictly pseudoconvex domains. https://doi.org/10.1007/s10455-012-9313-5

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