On the dynamical behaviour of the generalized Ricci flow

Abstract

Motivated by Müller-Haslhofer results on the dynamical stability and instability of Ricci-flat metrics under the Ricci flow, we obtain dynamical stability and instability results for pairs of Ricci-flat metrics and vanishing 3-forms under the generalized Ricci flow.

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

“…A Perelman-type F-functional for this was found in [19], and an expander entropy functional was found in [26]. Some recent results in the homogeneous setting have appeared [20], as well as a stability result near Ricci-flat metrics [23]. In [9] it was shown that the equation reduces to Ricci-Yang-Mills flow in the case of a U (1) principal bundle over a Riemann surface.…”