English

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.

Keywords

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