Balanced metrics on Cartan and Cartan–Hartogs domains

This paper consists of two results dealing with balanced metrics (in Donaldson terminology) on noncompact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in Loi and Zedda (Mathematische Annalen, 2011) we also provide the first example of complete, Kähler-Einstein and projectively induced metric g such that αg is not balanced for all α > 0.