On generalized Shen's square metric
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Abstract
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 $\pi$-vector field, we study some geometric objects associated with $\widetilde{L}(x,y)=\frac {(L+\mathfrak{B)}^2} {L}$ in terms of the objects of $L$, where $\mathfrak{B}$ is the associated $1$-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of $\widetilde{L}(x,y)$. Moreover, we calculate the curvature of the Barthel connection of $\widetilde{L}$. We characterize the non-degeneracy of the metric tensor of $\widetilde{L}(x,y)$.
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