On homogeneous HKT manifolds and the Einstein condition
Differential Geometry
2026-04-27 v1
Abstract
We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant HKT-Einstein metric, which is unique up to scaling. Furthermore, we determine for which invariant HKT metrics the torsion and the curvature of the Bismut connection are Bismut-parallel, showing that invariant strong HKT metrics have this property.
Cite
@article{arxiv.2604.22404,
title = {On homogeneous HKT manifolds and the Einstein condition},
author = {Lucio Bedulli and Lorenzo Marcocci},
journal= {arXiv preprint arXiv:2604.22404},
year = {2026}
}
Comments
19 pages, comments are welcome