New Cartan’s Tensors and Pseudotensors in a Generalized Finsler Space

Abstract

 In this work we defined a generalized Finsler space (GFN) as 2N-dimensional differentiable manifold with a non-symmetric basic tensor gij(x, x˙), which applies that symmetric part of h-covariant derivative of the first and the second kind is equal zero.  Based on non-symmetry of basic tensor, we obtained ten Ricci type identities, comparing to two kinds of covariant derivative of a tensor in Rund's sense. There appear two new curvature tensors and fifteen magnitudes, we called "curvature pseudotensors".