On generalized Shen's square metric

In this paper, following the pullback approach to global Finsler geometry, we investigate a coordinate-free study of Shen square metric in a more general
manner. Precisely, for a Finsler metric (M; L) admitting a concurrent π-vector field,
we study some geometric objects associated with Le(x; y) = (L+LB)2 in terms of the
objects of L, where B is the associated 1-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of Le(x; y). Moreover, we calculate the curvature of the Barthel connection of Le. We characterize the non-degeneracy of the metric tensor of Le(x; y)