Open AccessOn certain a generalized \(N_{|m}\) ̶ Recurrent Finsler space
Author(s) -
Abdalstar Ali Mohsen Saleem
Publication year - 2020
Publication title -
mağallaẗ ğāmi'aẗ 'adan li-l-'ulūm al-ṭabīyyaẗ wa-al-taṭbīqiyyaẗ
Language(s) - English
Resource type - Journals
eISSN - 2788-9327
pISSN - 1606-8947
DOI - 10.47372/uajnas.2020.n1.a17
Subject(s) - mathematics , curvature , space (punctuation) , weyl tensor , riemann curvature tensor , tensor field , tensor (intrinsic definition) , ricci decomposition , vector field , ricci curvature , pure mathematics , covariant transformation , zero (linguistics) , quaternionic projective space , mathematical physics , mathematical analysis , complex projective space , projective space , projective test , geometry , exact solutions in general relativity , computer science , linguistics , philosophy , operating system
A Finsler space \(F_n\) for which the normal projective curvature tensor \(N_{jkh}^i\) satisfies \(N_{jkh|m}^i = λ_m N_{jkh}^i + μ_m (δ_h^i g_{jk} - δ_k^i g_{jh} ), N_{jkh}^i ≠ 0\), where \(λ_m\) and \(μ_m\) are non-zero covariant vectors field, will be called a generalized \(N_{|m}\) ̶ recurrent space. The curvature vector \(H_k\), the curvature scalarH and Ricci tensor \(N_{jk}\) are non-vanishing. When the generalized \(N_{|m}\) ̶ recurrent space is affinely connected space and under certain conditions, we obtain various results. Also, in generalized \(N_{|m}\) ̶ recurrent space, Weyl's projective curvature tensoris a generalized recurrent tensor.