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arXiv · 2604.22404

On homogeneous HKT manifolds and the Einstein condition

Lucio Bedulli·Lorenzo Marcocci
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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.

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Lucio Bedulli, Lorenzo Marcocci. 2026-04-24. On homogeneous HKT manifolds and the Einstein condition. https://arxiv.org/abs/2604.22404

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