2007/08/23 by Martin Laubinger, Laubinger, Martin · 1 citation
Engineering · Mathematics · #32Q60 #58D27 #81R10 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Geometry (math.DG) #Elasticity and Wave Propagation #FOS: Mathematics #Mathematics and Applications #math.CV #math.DG #msc:32Q60 #msc:58D27 #msc:81R10
paper · pdf · doi:10.48550/arxiv.0708.3261
17 pages
arxiv created 2007/08/23 · openalex publication_date 2007/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H1(M,G). On the other hand, if M=Σis a closed Riemann surface, there is a correspondence between holomorphic principal G-bundles over Σand coadjoint orbits in the dual of a central extension of the Lie algebra C^∞(Σ, \g). We review these results and provide the details of an integrability condition for almost complex structures on smoothly trivial bundles. This article is a shortened version of the author's Diplom thesis.