On the Petersson-Weil metric for the moduli space of Hermite-Einstein bundles and its curvature. (English) Zbl 0771.53037

The Petersson-Weil metric is a natural Kähler metric on Hermite- Einstein vector bundles on complex surfaces. The main purpose of this paper is to prove (in any dimension) an explicit formula for the curvature tensor of the Petersson-Weil metric on the base of a family of Hermite-Einstein vector bundles in a very short way. The authors make use only of the curvature form on the total space which in fact contains the harmonic representations of the Kodaira-Spencer classes.
Reviewer: N.Bokan (Beograd)


53C55 Global differential geometry of Hermitian and Kählerian manifolds
32G13 Complex-analytic moduli problems
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