BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.
Popovici, Limits of projective manifolds under holomorphic deformat ions: Hodge numbers and strongly Gauduchon metrics, Invent
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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.