On the Geometry of Connections with Totally Skew-Symmetric Torsion on Manifolds with Additional Tensor Structures and Indefinite Metrics

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric.