Abstract
We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine manifolds is shown. Also shown, in the context of affine manifolds, is a bijective correspondence between polystable flat pairs and solutions of the vortex equation. [Figure not available: see fulltext.]
Original language | English (US) |
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Pages (from-to) | 159-175 |
Number of pages | 17 |
Journal | Arabian Journal of Mathematics |
Volume | 2 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1 2013 |
All Science Journal Classification (ASJC) codes
- General Mathematics