Abstract

In the present communication, we have derived Bianchi and Veblen identities along with a few more related results in a recurrent and generalized n^th-recurrent Finsler space with Cartan’s curvature tensor field. A Finsler space  $F_n$ whose Cartan's third curvature tensor $R_{jkh}^i$ satisfies the condition $R_{jkh|m_1|m_2|\dots |m_n}^i={\lambda }_{m_1{m}_2\dots m_n}{R}_{jkh}^i+{\mu }_{m_1{m}_2\dots m_n}({\delta }_h^i{g}_{jk}-{\delta }_k^i{g}_{jh})$, where $R_{jkh}^i$≠0 and $|m_1|m_2|\dots |m_n$ are h-covariant differentiation (Cartan's second kind covariant differential operator) with respect to x^m to nth order, ${\lambda }_{m_1{m}_2\dots m_n}$ and ${\mu }_{m_1{m}_2\dots m_n}$ is recurence tensors fields.