Year 2020, Volume , Issue 32, Pages 30 - 39 2020-09-30

Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space

Adel Mohammed Ali AL-QASHBARΔ° [1]


The purpose of the present paper is to consider and study a certain identities for some generalized curvature tensors in ℬ-recurrent Finsler space 𝐹𝑛 in which Cartan’s second curvature tensor π‘ƒπ‘—π‘˜β„Žπ‘– satisfies the generalized of recurrence condition with respect to Berwald’s connection parameters Gπ‘˜β„Žπ‘– which given by the condition β„¬π‘šπ‘ƒπ‘—π‘˜β„Žπ‘–=πœ†π‘š π‘ƒπ‘—π‘˜β„Žπ‘–+πœ‡π‘š( π›Ώβ„Žπ‘– π‘”π‘—π‘˜βˆ’ π›Ώπ‘˜π‘– π‘”π‘—β„Ž), where β„¬π‘š is covariant derivative of first order (Berwald’s covariant differential operator ) with respect to π‘₯π‘š, it’s called a generalized ℬP-recurrent space. We shall denote it briefly by 𝐺ℬ𝑃-𝑅𝐹𝑛. We have obtained Berwald’s covariant derivative of first order for the h(v)-torsion tensor π‘ƒπ‘˜β„Ž 𝑖, the deviation tensor π‘ƒβ„Ž 𝑖 and the covariant derivative of the tensor π»π‘˜π‘.β„Ž (in the sense of Berwald), also we find some theorems of the R-Ricci tensor π‘…π‘—π‘˜ and the curvature vector 𝑅𝑗in our space. We obtained the necessary and sufficient condition for Berwald’s covariant derivative of Weyl’s projective curvature tensor π‘Šπ‘—π‘˜β„Žπ‘– and its torsion tensor π‘Šπ‘˜β„Žπ‘– in our space. Also, we have proved that in 𝐺ℬ𝑃-𝑅𝐹𝑛, Cartan’s second curvature tensor π‘ƒπ‘—π‘˜β„Žπ‘– and the v(hv)-torsion tensor π‘ƒπ‘˜β„Žπ‘– for 𝑛=4 .
Finsler space, Cartan’s second curvature tensor π‘ƒπ‘—π‘˜β„Žπ‘–, Generalized ℬ𝑃-recurrent space, Weyl’s projective curvature tensor π‘Šπ‘—π‘˜β„Žπ‘–, Cartan’s fourth curvature tensor π‘…π‘—π‘˜β„Žπ‘–
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Primary Language en
Subjects Mathematics
Journal Section Research Article
Authors

Orcid: 0000-0002-4045-4520
Author: Adel Mohammed Ali AL-QASHBARΔ° (Primary Author)
Institution: Department of Mathematic, Faculty of Educ. -Aden, University of Aden
Country: Yemen


Supporting Institution Department of Mathematics, Faculty of Education -Aden, University of Aden.
Dates

Publication Date : September 30, 2020

Bibtex @research article { jnt802259, journal = {Journal of New Theory}, issn = {}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2020}, volume = {}, pages = {30 - 39}, doi = {}, title = {Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space}, key = {cite}, author = {Al-qashbariΜ‡, Adel Mohammed Ali} }
APA Al-qashbariΜ‡, A . (2020). Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space . Journal of New Theory , (32) , 30-39 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/56973/802259
MLA Al-qashbariΜ‡, A . "Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space" . Journal of New Theory (2020 ): 30-39 <https://dergipark.org.tr/en/pub/jnt/issue/56973/802259>
Chicago Al-qashbariΜ‡, A . "Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space". Journal of New Theory (2020 ): 30-39
RIS TY - JOUR T1 - Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space AU - Adel Mohammed Ali Al-qashbariΜ‡ Y1 - 2020 PY - 2020 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 30 EP - 39 VL - IS - 32 SN - -2149-1402 M3 - UR - Y2 - 2020 ER -
EndNote %0 Journal of New Theory Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space %A Adel Mohammed Ali Al-qashbariΜ‡ %T Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space %D 2020 %J Journal of New Theory %P -2149-1402 %V %N 32 %R %U
ISNAD Al-qashbariΜ‡, Adel Mohammed Ali . "Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space". Journal of New Theory / 32 (September 2020): 30-39 .
AMA Al-qashbariΜ‡ A . Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. JNT. 2020; (32): 30-39.
Vancouver Al-qashbariΜ‡ A . Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. Journal of New Theory. 2020; (32): 30-39.

Authors of the Article
Adel Mohammed Ali AL-QASHBARΔ° [1]