In this article, we study the set of balanced metrics given in Donaldson's terminology (J. Diff. Geometry 59:479-522, 2001) on a compact complex manifold M which are homothetic to a given balanced one. This question is related to various properties of the Tian-Yau-Zelditch approximation theorem for Kähler metrics. We prove that this set is finite when M admits a non-positive Kähler-Einstein metric, in the case of non-homogenous toric Kähler-Einstein manifolds of dimension ≤ 4 and in the case of the constant scalar curvature metrics found in Arezzo and Pacard (Acta. Math. 196(2):179-228, 2006; Ann. Math. 170(2):685-738, 2009).
On homothetic balanced metrics
LOI, ANDREA;ZUDDAS, FABIO
2012-01-01
Abstract
In this article, we study the set of balanced metrics given in Donaldson's terminology (J. Diff. Geometry 59:479-522, 2001) on a compact complex manifold M which are homothetic to a given balanced one. This question is related to various properties of the Tian-Yau-Zelditch approximation theorem for Kähler metrics. We prove that this set is finite when M admits a non-positive Kähler-Einstein metric, in the case of non-homogenous toric Kähler-Einstein manifolds of dimension ≤ 4 and in the case of the constant scalar curvature metrics found in Arezzo and Pacard (Acta. Math. 196(2):179-228, 2006; Ann. Math. 170(2):685-738, 2009).
| File | Dimensione | Formato | |
|---|---|---|---|
|
hombalanced.pdf
Solo gestori archivio
Tipologia:
versione editoriale (VoR)
Dimensione
1.23 MB
Formato
Adobe PDF
|
1.23 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
