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On homothetic balanced metrics

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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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Authors and Affiliations

  1. Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, Trieste, Italy

    Claudio Arezzo

  2. Dipartimento di Matematica, Università di Cagliari, Parma, Italy

    Andrea Loi

  3. Dipartimento di Matematica, Università di Parma, Parco Area Delle Scienze 53/A, Parma, Italy

    Claudio Arezzo & Fabio Zuddas

Authors
  1. Claudio Arezzo
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  2. Andrea Loi
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  3. Fabio Zuddas
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Correspondence to Claudio Arezzo.

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Arezzo, C., Loi, A. & Zuddas, F. On homothetic balanced metrics. Ann Glob Anal Geom 41, 473–491 (2012). https://doi.org/10.1007/s10455-011-9295-8

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