Geodesic
Commutation formulas for $\delta$-differentiation in a generalized Finsler space
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 277

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In this work we define a generalized Finsler space $\mathbb{GF}_N$ as $N$- dimensional differentiable manifold on which a non-symmetric basic tensor $g_{ij}(x,\dot{x})$ is defined by virtue (1.3). Some basic properties of $\mathbb{GF}_N$ are given ($\S1)$. Based on non-symmetry of basic tensor, we define $(\S2)$ two kinds of covariant derivative of a tensor in the Rund's sense and obtain 10 Ricci type identities. In these identities appear 3 curvature tensors and 15 magnitudes, which we call "curvature pseudotensors" in $\mathbb{GF}_N$. All mentioned curvature tensors and pseudotensors reduce to known curvature tensor in usual Finsler space $\mathbb{F}_N$. The cited Ricci type identities are proved by total induction method in a general case.
Classification : 53A45 53B05 53B40
Keywords: Generalized Finsler spaces, Ricci type identities, Covariant derivative, Non-symmetric connection, Curvature tensor, Curvature pseudotensor. 
Svetislav M. Minčić; Miljan Lj. Zlatanović. Commutation formulas for $\delta$-differentiation in a generalized Finsler space. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 277 . http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a6/
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     title = {Commutation formulas for $\delta$-differentiation in a generalized {Finsler} space},
     journal = {Kragujevac Journal of Mathematics},
     pages = {277 },
     year = {2011},
     volume = {35},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a6/}
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