Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold

Abstract

The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of (σ,τ)-Hermite–Yang–Mills metric in differential geometry and the analytic (σ,τ)-stability in algebraic geometry. The proof of the theorem relies on the flow method and the Uhlenbeck–Yau’s continuity method.

Keywords

• analytic (<i>σ</i>,<i>τ</i>)-stability
• quiver bundle
• (<i>σ</i>,<i>τ</i>)-Hermite–Yang–Mills metric
• non-compact manifold