A connection with skew symmetric torsion and K\"ahler curvature tensor on quasi-K\"ahler manifolds with Norden metric

Abstract

There is considered a connection with skew symmetric torsion on a quasi-K\"ahler manifold with Norden metric. Some necessary and sufficient conditions are derived for the corresponding curvature tensor to be K\"ahlerian. In the case when this tensor is K\"ahlerian, some relations are obtained between its scalar curvature and the scalar curvature of other curvature tensors. Conditions are given for the considered manifolds to be isotropic-K\"ahler.