Frame flows on manifolds with pinched negative curvature
The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.