The paper establishes a canonical reduction theorem and classifies complete simply-connected Bismut-Ambrose-Singer manifolds in homogeneous settings plus their pluriclosed variants.
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BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.
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On Bismut--Ambrose--Singer manifolds
The paper establishes a canonical reduction theorem and classifies complete simply-connected Bismut-Ambrose-Singer manifolds in homogeneous settings plus their pluriclosed variants.
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Curvature characterization of Hermitian manifolds with Bismut parallel torsion
BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.