A study of recurrent Finsler spaces of higher order with Cartan’s Curvature Tensor

Abstract

In the present communication, we have derived Bianchi and Veblen identities along with a few more related results in a recurrent and generalized nth-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 \(R_{jkh|m_1|m_2|…|m_n}^{i} = λ_{m_1m_2…m_n} R_{jkh}^{i} + μ_{m_1m_2…m_n} (δ_{h}^{i} g_{jk} - δ_{k}^{i} g_{jh})\), where \(R_{jkh}^i\)≠0 and \(|m_1 |m_2 |…|m_n\) are h-covariant differentiation (Cartan's second kind covariant differential operator) with respect to x^m to nth order, \(λ_{m_1 m_2…m_n }\) and \(μ_{m_1 m_2…m_n }\) is recurence tensors fields.