Global attraction of standard Bismut-flat metrics on simple Lie groups

Determine whether the standard bi-invariant Bismut-flat metrics on compact simple Lie groups are global attractors for the homogeneous generalized Ricci flow.

Background

The paper proves dynamical stability of standard bi-invariant Bismut-flat metrics on compact, simply connected, semisimple Lie groups for sufficiently close initial data. It also constructs non-standard Bismut-flat metrics that are dynamically unstable, thereby disproving the broader conjecture that standard Bismut-flat metrics are always global attractors.

The authors distinguish the unresolved simple-group case from the semisimple case: although instability examples show that global attraction fails in general for semisimple groups, it remains unknown whether the standard metrics retain the global-attractor property when the underlying compact Lie group is simple. Establishing this would clarify the global dynamics beyond the local stability result proved in the paper.

References

As far as the authors are aware, it remains open whether the standard bi-invariant Bismut-flat metrics on simple Lie groups are global attractors.

— Homogeneous Generalized Ricci flows II  (2608.25619 - Fusi et al., 26 Aug 2026) in Section 1, Introduction; Section 6, immediately following Theorem 6.1

Numerical analysis leads one to conjecture that $(#1 G \times \Delta #1 K)$-homogeneous generalized Ricci flows in the unstable manifold of $#1 G(g_{1,3,1},\beta)$ converge to the Bismut-flat metric $#1 G(g_{1,1,0},0)$. Such a heteroclinic orbit would yield an interesting eternal solution to the homogeneous generalised Ricci flow on $#1 G$.

— Homogeneous Generalized Ricci flows II  (2608.25619 - Fusi et al., 26 Aug 2026) in Section 6, Dynamically unstable Bismut-flat metrics, final remarks of the section