Dimensional reduction of the perturbed Hermitian-Einstein equation

2004/05/12 by Steven B. Bradlow, James F. Glazebrook, Franz W. Kamber
Mathematics · #math.DG #msc:58D27 #msc:22B40 #msc:32L10 #msc:58G10 #msc:53C07

paper · pdf

published as Proc. in Global Analysis, Diff. Geometry and Lie Algebras, Balkan Geometry Press, Bucharest 2001, pp. 43-62 · 13 pages

arxiv created 2004/05/12 · arxiv updated 2009/12/01

Abstract

Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the holomorphic bundles, there is a dimensional reduction procedure which reduces these equations to a system of equations on the base, known as the twisted coupled vortex equations.

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