BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.
Bismut, A local index theorem for non-K¨ ahler manifolds, Math
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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.