Dimensional reduction of the perturbed Hermitian-Einstein equation

Details Dimensional reduction of the perturbed Hermitian-Einstein equation Dimensional reduction of the perturbed Hermitian-Einstein equation

2004-05-12

arxiv.org/abs/math/0405205v1

Proc. in Global Analysis, Diff. Geometry and Lie Algebras, Balkan Geometry Press, Bucharest 2001, pp. 43-62

Mathematics

Differential Geometry

13 pages

Scientific paper

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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