Two new families of Finsler connections on even-dimensional manifolds

Abstract

Let $F^{2n}=(M,M^{\prime },F^{\ast })$ be an even-dimensional pseudo-Finsler manifold. We construct an almost hypercomplex structure on any chart domain of a certain atlas of $M^{\prime }$ by using a considered non-linear connection. Then by using the almost hypercomplex structure we define two new families of Finsler connections. Also we show that for any Finsler connection $\nabla$ there exists a linear connection $D$ such that the local almost hypercomplex structure is parallel with respect to it.