Commutation formulas for $\delta$-differentiation in a generalized Finsler space

Svetislav M. Minčić ; Miljan Lj. Zlatanović

Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 277

Résumé

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.

Détail

Classification : 53A45 53B05 53B40
Keywords: Generalized Finsler spaces, Ricci type identities, Covariant derivative, Non-symmetric connection, Curvature tensor, Curvature pseudotensor.