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arXiv · 1103.6158

Some remarks on the Kaehler geometry of LeBrun's Ricci flat metrics on C^2

Andrea Loi·Michela Zedda·Fabio Zuddas
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Abstract

In this paper we investigate the balanced condition (in the sense of Donaldson) and the existence of an Englis expansion for the LeBrun's metrics on $C^2$. Our first result shows that a LeBrun's metric on $C^2$ is never balanced unless it is the flat metric. The second one shows that an Englis expansion of the Rawnsley's function associated to a LeBrun's metric always exists, while the coefficient $a_3$ of the expansion vanishes if and only if the LeBrun's metric is indeed the flat one.

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Andrea Loi, Michela Zedda, Fabio Zuddas. 2011-03-31. Some remarks on the Kaehler geometry of LeBrun's Ricci flat metrics on C^2. https://arxiv.org/abs/1103.6158

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