On the cone of strong Kähler with torsion metrics (Q1681828)

This paper examines special metrics on compact complex manifolds, focusing on the notion of super strong Kähler with torsion metrics. This condition is related to the strong Kähler with torsion one in the same manner as the strongly Gauduchon condition is related to the Gauduchon one. The author provides sufficient and necessary conditions so that evert strong Kähler with torsion metric on a compact manifold is super strong Kähler with torsion. It is also shown that these conditions are verified on compact complex manifolds satisfying the \(\partial\overline{\partial}\)-lemma but not on 6-dimensional compact complex nilmanifolds.