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.
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.
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