Harmonic Hermitian Structures on Riemannian Manifolds with Skew Torsion

Pseudo-harmonic Hermitian structures on Weyl manifolds

“…These structures are genuine harmonic maps from (M, g) into (Z, g t ), and we refer to [11] for basic facts about harmonic maps. This point of view is taken in [8,9] where the problem of when an almost-Hermitian structure on a Riemannian four-manifold is a harmonic map from the manifold into its twistor space is discussed. In [8], the metric g t is defined via the Levi-Civita connection; it is defined by means of a metric connection with totally skew-symmetric torsion in [9].…”