A connection with skew symmetric torsion and Kähler curvature tensor on quasi-Kähler manifolds with Norden metric

Abstract

There is considered a connection with skew symmetric torsion on a quasi-Kähler manifold with Norden metric. Some necessary and sufficient conditions are derived for the corresponding curvature tensor to be Kählerian. In the case when this tensor is Kählerian, 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-Kähler.

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• On canonical-type connections on almost contact complex Riemannian manifolds
• On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
• Canonical connection on quasi-Kaehler manifolds with Norden metric
• On some Lie groups as 5-dimensional almost contact B-metric manifolds with three natural connections