On homothetic balanced metrics |
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Authors: | Email author" target="_blank">Claudio?ArezzoEmail author Andrea?Loi Fabio?Zuddas |
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Institution: | 1.Abdus Salam International Center for Theoretical Physics,Trieste,Italy;2.Dipartimento di Matematica,Università di Cagliari,Parma,Italy;3.Dipartimento di Matematica,Università di Parma,Parma,Italy |
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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). |
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