  The $B$-connection on almost complex manifolds with Norden metric is an
analogue of the first canonical connection of Lihnerovich in Hermitian
geometry. In the present paper it is considered a $B$-connection in the class
of the quasi-K\"ahler manifold with Norden metric. Some necessary and
sufficient conditions are derived for the corresponding curvature tensor to be
K\"ahlerian. Curvature properties for this connection are obtained. Conditions
are given for the considered manifolds to be isotropic-K\"ahler.

Differential Geometry