On the geometry of the $B$-connection on quasi-Kähler manifolds with Norden metric

Abstract

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-Kähler manifold with Norden metric. Some necessary and sufficient conditions are derived for the corresponding curvature tensor to be Kählerian. Curvature properties for this connection are obtained. Conditions are given for the considered manifolds to be isotropic-Kähler.

Cited by in corpus (2)

• On canonical-type connections on almost contact complex Riemannian manifolds
• On some Lie groups as 5-dimensional almost contact B-metric manifolds with three natural connections