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We consider an almost complex manifold with Norden metric (i. e. a metricwith respect to which the almost complex structure is an anti-isometry). Onsuch a manifold we study a linear connection preserving the almost complexstructure and the metric and having a totally skew symmetric torsion tensor (i.e. a 3-form). We prove that if a non-Kaehler almost complex manifold withNorden metric admits such connection then the manifold is quasi-Kaehlerian (i.e. has non-integrable almost complex structure). We prove that this connectionis unique, determine its form, and construct an example of it on a Lie group.We consider the case when the manifold admits a connection with paralleltotally skew-symmetric torsion and the case when such connection has a Kaehlercurvature tensor. We get necessary and sufficient conditions for an isotropicKaehler manifold with Norden metric.

On the geometry of the connection with totally skew-symmetric torsion on almost complex manifolds with Norden metric