On some Lie groups as 5-dimensional almost contact B-metric manifolds with three natural connections

Abstract

Almost contact manifolds with B-metric are considered. There are studied three natural connections (i.e. linear connections preserving the structure tensors) determined by conditions for their torsions. These connections are investigated on a family of Lie groups considered as 5-dimensional almost contact B-metric manifolds.

11 pages

References in corpus (2)

• A connection with skew symmetric torsion and Kähler curvature tensor on quasi-Kähler manifolds with Norden metric
• On the geometry of the $B$-connection on quasi-Kähler manifolds with Norden metric