Balanced metrics on C^n

CUCCU, FABRIZIO;LOI, ANDREA

2007-01-01

---

Abstract

Let g be a Kaehler metric on C^n. In this paper we prove that if g is rotation invariant and balanced (in the sense of Donaldson) then, up to biholomorphic isometries, g equals the Euclidean metric. The proof of our theorem is based on Calabi's diastasis function and on the characterization of the exponential function due to Miles and Williamson.