Every homogeneous hypercomplex manifold with transitive compact Lie group action admits a unique invariant HKT-Einstein metric up to scaling, and invariant strong HKT metrics have Bismut-parallel torsion and curvature.
2023.Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow
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Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, together with a splitting theorem for compact pluriclosed Calabi-Yau-with-torsion manifolds.
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On homogeneous HKT manifolds and the Einstein condition
Every homogeneous hypercomplex manifold with transitive compact Lie group action admits a unique invariant HKT-Einstein metric up to scaling, and invariant strong HKT metrics have Bismut-parallel torsion and curvature.
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Pluriclosed manifolds with parallel Bismut torsion
Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, together with a splitting theorem for compact pluriclosed Calabi-Yau-with-torsion manifolds.