A study of recurrent Finsler spaces of higher order with Cartan’s Curvature Tensor
University of Aden Journal of Natural and Applied Sciences,
Vol. 27 No. 2 (2023),
31-10-2023
Page 291-300
DOI:
https://doi.org/10.47372/uajnas.2023.n2.a10
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.
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Finsler space \(F_n\), Generalized R - \(n^{th}\)-recurrent space, Cartan’s covariant derivative of higher order, Cartan’s third curvature tensor \(R_{jkh}^i\), Cartan’s second curvature tensor \(P_{jkh}^i\)
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