Flat bundles on affine manifolds

Indranil Biswas, John Loftin, Matthias Stemmler

Research output: Contribution to journalReview articlepeer-review

6 Scopus citations


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 languageEnglish (US)
Pages (from-to)159-175
Number of pages17
JournalArabian Journal of Mathematics
Issue number2
StatePublished - Jun 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


Dive into the research topics of 'Flat bundles on affine manifolds'. Together they form a unique fingerprint.

Cite this