Poisson metrics and Higgs bundles over noncompact Kähler manifolds

2021/09/04 by Di Wu, Xi Zhang, Wu, Di +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2109.01776

openalex publication_date 2021/09/04 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing Corlette-Donaldson-Hitchin-Simpson's nonabelian Hodge correspondence to noncompact Kähler manifolds setting.

Citations

• The Self-Duality Equations on a Riemann Surface
• Harmonic Mappings of Riemannian Manifolds
• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules
• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Projectively flat bundles and semi-stable Higgs bundles
• The limit of the harmonic flow on flat complex vector bundle

Related

• Higgs bundles on Sasakian manifolds
• Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds
• A note of semistable Higgs bundles over compact Kähler manifolds
• Higgs bundles over non-compact Gauduchon manifolds
• Higgs bundles and flat connections over compact Sasakian manifolds