Generalized Ricci flow on aligned homogeneous spaces

The fixed points of the generalized Ricci flow are the Bismut Ricci flat (BRF) metrics, i.e., a generalized metric (g,H) on a manifold M, where g is a Riemannian metric and H a closed 3-form, such that H is g-harmonic and Rc (g) =1/4H(g)(2). Given two standard Einstein homogeneous spaces G(i)/K, where each G(i) is a compact simple Lie group and K is a closed subgroup of them holding some extra assumption, we consider M=G(1)xG(2)/triangle K. Recently, Lauret and Will proved the existence of a BRF metric on anyof these spaces. We proved that this metric is always asymptotically stable for the generalized Ricci flow on M among a subset of G-invariant metrics and, if G(1)=G(2), then it is globally stable.