ON GRAUERT'S EXAMPLES OF COMPLETE KÄHLER METRICS

Gehlawat, S and Verma, K (2022) ON GRAUERT'S EXAMPLES OF COMPLETE KÄHLER METRICS. In: Proceedings of thcited By 0e American Mathematical Society, 150 (7). pp. 2925-2936.

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Abstract

Grauert showed that the existence of a complete Kähler metric does not characterize domains of holomorphy by constructing such metrics on the complements of complex analytic sets in a domain of holomorphy. In this note, we study the holomorphic sectional curvatures of such metrics in two prototype cases namely, Cn \ {0}, n ≥ 2 and BN \ A, N ≥ 2 and A ⊂ BN is a hyperplane of codimension at least two. This is done by computing the Gaussian curvature of the restriction of these metrics to the leaves of a suitable holomorphic foliation in these two examples. We also examine this metric on the punctured plane C∗ and show that it behaves very differently in this case.

Item Type:	Journal Article
Publication:	Proceedings of thcited By 0e American Mathematical Society
Publisher:	American Mathematical Society
Additional Information:	The Copyright of this article belongs to the Authors.
Keywords:	complete Kähler metric; Holomorphic sectional curvature
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Jul 2022 05:37
Last Modified:	01 Jul 2022 05:37
URI:	https://eprints.iisc.ac.in/id/eprint/74149

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