Abstract
Given the class of Finsler spaces with Lorentzian signature [Formula: see text] on a manifold [Formula: see text] endowed with a timelike vector field [Formula: see text] satisfying [Formula: see text] at any point [Formula: see text] of the slit tangent bundle, a pseudo-Riemannian metric defined on [Formula: see text] of signature [Formula: see text] is associated to the fundamental tensor [Formula: see text]. Furthermore, an affine, torsion free connection is associated to the Chern connection determined by [Formula: see text]. The definition of the average connection does not make use of [Formula: see text]. Therefore, there is no direct relation between these two averaged objects.
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