On the slit tangent bundle of Finsler manifolds, we introduce a class of metrics and study the relation between Levi-Civita connection, Vaisman connection, vertical foliation, and Reinhart spaces. We show that the Levi-Civita and the Vaisman connections induce the same connections in the structural bundle if and only if the base manifold is Landsbergian. Moreover every foliated Reinhart manifold reduces to a Riemannian manifold.
展开▼
