Ricci-Yang-Mills flow on surfaces and pluriclosed flow on elliptic fibrations

TL;DR

This paper analyzes the Ricci-Yang-Mills flow on torus bundles over Riemann surfaces, providing a comprehensive understanding of its global behavior and convergence, which also informs solutions to related geometric flows with symmetry.

Contribution

It offers a complete description of the global existence and convergence for the Ricci-Yang-Mills flow on specific fiber bundles, connecting it to generalized Ricci and pluriclosed flows.

Findings

Established conditions for global existence

Proved convergence results for the flow

Linked flow solutions to symmetric geometric structures

Abstract

We give a complete description of the global existence and convergence for the Ricci-Yang-Mills flow on $T^k$ bundles over Riemann surfaces. These results equivalently describe solutions to generalized Ricci flow and pluriclosed flow with symmetry.