The Chen-Nie conjecture for canonical metric connections is verified for complex nilmanifolds with nilpotent J and for Bismut torsion-parallel manifolds.
Boothby, Hermitian manifolds with zero curvature, Michigan Math
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Canonical metric connections with constant holomorphic sectional curvature
The Chen-Nie conjecture for canonical metric connections is verified for complex nilmanifolds with nilpotent J and for Bismut torsion-parallel manifolds.