Generalized Ricci flow on aligned homogeneous spaces

Abstract 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 $\operatorname{Rc}(g)=\tfrac{1}{4} H_g^2$ . 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 $M=G_1\times G_2/\Delta K$ . Recently, Lauret and Will proved the existence of a BRF metric on any of 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.