Natural connections with torsion expressed by the metric tensors on   almost contact manifolds with B-metric
  On a main class of the almost contact manifolds with B-metric, it is described the family of the linear connections preserving the manifold's structures by 4 parameters. In this family there are determined the canonical-type connection and the connection with zero parameters. 
Mancho Manev, Miroslava Ivanova
math.DG