2010/02/05 by Indranil Biswas, Biswas, Indranil, Graeme Wilkin +1
Mathematics · #14F05 #58E05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG #msc:14F05 #msc:58E05
paper · pdf · doi:10.48550/arxiv.1002.1108
16 pages, to appear Geometriae Dedicata
arxiv created 2010/02/05 · openalex publication_date 2010/02/05 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fix a C^∞ principal G--bundle E0G on a compact connected Riemann surface X, where G is a connected complex reductive linear algebraic group. We consider the gradient flow of the Yang--Mills--Higgs functional on the cotangent bundle of the space of all smooth connections on E0G. We prove that this flow preserves the subset of Higgs G--bundles, and, furthermore, the flow emanating from any point of this subset has a limit. Given a Higgs G--bundle, we identify the limit point of the integral curve passing through it. These generalize the results of the second named author on Higgs vector bundles.