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Some remarks on the Kähler geometry of the Taub-NUT metrics

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Abstract

In this article, we investigate the balanced condition and the existence of an Engliš expansion for the Taub-NUT metrics on \({\mathbb{C}^2}\) . Our first result shows that a Taub-NUT metric on \({\mathbb{C}^2}\) is never balanced unless it is the flat metric. The second one shows that an Engliš expansion of the Rawnsley’s function associated to a Taub-NUT metric always exists, while the coefficient a 3 of the expansion vanishes if and only if the Taub-NUT metric is indeed the flat one.

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Loi, A., Zedda, M. & Zuddas, F. Some remarks on the Kähler geometry of the Taub-NUT metrics. Ann Glob Anal Geom 41, 515–533 (2012). https://doi.org/10.1007/s10455-011-9297-6

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