Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow

TL;DR

This paper investigates the stability of Bismut flat metrics on certain compact Lie groups under the pluriclosed flow, showing they are globally stable and ruling out specific Einstein metrics on C-spaces.

Contribution

It computes the (1,1)-Aeppli cohomology of compact simply-connected Lie groups and establishes the stability of Bismut flat metrics under the pluriclosed flow.

Findings

Bismut flat metrics are globally stable on certain manifolds.

No non-flat homogeneous Bismut Hermitian Einstein metrics exist on C-spaces.

Computed the (1,1)-Aeppli cohomology for compact simply-connected Lie groups.

Abstract

We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie groups. From this, we deduce that the Bismut flat metrics on the compact Bismut flat manifolds with finite fundamental group are globally stable for the pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on C-spaces.