In this article, we investigate the balanced condition and the existence of an Engliš expansion for the Taub-NUT metrics on ℂ^2. Our first result shows that a Taub-NUT metric on 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.

Some remarks on the Kähler geometry of the Taub-NUT metrics / Loi, Andrea; Zedda, Michela; Zuddas, Fabio. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 41:(2012), pp. 515-533. [10.1007/s10455-011-9297-6]

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

ZEDDA, MICHELA;
2012

Abstract

In this article, we investigate the balanced condition and the existence of an Engliš expansion for the Taub-NUT metrics on ℂ^2. Our first result shows that a Taub-NUT metric on 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.
Some remarks on the Kähler geometry of the Taub-NUT metrics / Loi, Andrea; Zedda, Michela; Zuddas, Fabio. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 41:(2012), pp. 515-533. [10.1007/s10455-011-9297-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2838534
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