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on a manifold
is called strong KT if its fundamental 
-form 
is
-closed. We review some properties
of strong KT metrics. Known examples of compact
manifolds endowed with this type of Hermitian structures are also reviewed.
Key Words: Hermitian metric, torsion, Bismut connection, blow-up, resolution.
2000 Mathematics Subject Classification: Primary: 53C55,
Secondary: 53C25, 32C10.
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