Mathematics > Differential Geometry
arXiv:2606.20833 (math)
[Submitted on 18 Jun 2026]
Abstract:A classification of all invariant Hermitian structures with parallel Bismut torsion on most flag manifolds is given. More precisely, we prove that on a flag manifold $M=G/H$ such that $G$ is simple and different from $\mathrm{E}_6$, $\mathrm{E}_7$, $\mathrm{E}_8$ if $H$ is non-abelian, a $G$-invariant Hermitian structure on $M$ has parallel Bismut torsion if and only if the metric is either Kähler or a multiple of the Killing or standard metric.
Submission history
From: Martiniano Faure [view email]
[v1]
Thu, 18 Jun 2026 18:20:44 UTC (445 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.





















