Generalized Ricci flow on aligned homogeneous spaces

Abstract

The fixed points of the generalized Ricci flow are the Bismut Ricci flat 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 $\mathrm{Rc}(g)=\frac{1}{4}{H}_g^2$. 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 Bismut Ricci flat 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.

References in corpus (3)

• Infinite families of homogeneous Bismut Ricci flat manifolds
• Classification of generalized Einstein metrics on 3-dimensional Lie groups
• Einstein metrics on homogeneous spaces $H\times H/\Delta K$