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Connections on principal bundles over Kähler manifolds with antiholomorphic involution
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Indranil Biswas
Published/Copyright:
November 18, 2005
Abstract
Let M be a connected compact Kähler manifold equipped with an antiholomorphic involution τ. Let G be a complex reductive group; fix a real structure on G. We consider holomorphic principal G -bundles over M equipped with a lift of τ as an antiholomorphic involution of the total space of EG . We extend the notion of polystability to such bundles with involution and prove that polystability is equivalent to the existence of an Einstein-Hermitian connection compatible with the involution. We also give a criterion for such a bundle over a compact Riemann surface to have a holomorphic connection compatible with the involution.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Connections on principal bundles over Kähler manifolds with antiholomorphic involution
- Uniform distribution of the fractional part of the average prime divisor
- Analysis of the horizontal Laplacian for the Hopf fibration
- Algebraic inclusions of Moufang polygons
- Topological equivalence of linear representations for cyclic groups: II
- Capacities associated with Dirichlet space on an infinite extension of a local field
- The configuration space of arachnoid mechanisms
