Vanishing of the shifted Courant-Nijenhuis torsion is the strongest tensorial integrability condition for skew-symmetric endomorphisms of the generalized tangent bundle.
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A note on the shifted Courant-Nijenhuis torsion
Vanishing of the shifted Courant-Nijenhuis torsion is the strongest tensorial integrability condition for skew-symmetric endomorphisms of the generalized tangent bundle.