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

Year 2020, Issue: 32, 30 - 39, 30.09.2020

Abstract

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 .

Supporting Institution

Department of Mathematics, Faculty of Education -Aden, University of Aden.

References

  • P. N. Pandey, S. Saxena, A. Goswani, On A Generalized H-recurrent Space, Journal of International Academy of Physical Sciences 15 (2011) 201-211.
  • Z. Ahsan, M. Ali, On Some Properties of W-curvature Tensor, Palestine Journal of Mathematics, Palestine 3(1) (2014) 61-69.
  • F. Y. A. Qasem, On Transformation in Finsler Spaces, D. Phil Thesis, University of Allahabad, (Allahabad) (India) (2000).
  • M. Matsumoto, On h-isotropic and Ch-recurrent Finsler, Journal of Mathematics of Kyoto University 11 (1971), 1- 9.
  • F. Y. A. Qasem, A. A. M. Saleem, On π‘Šπ‘—π‘˜β„Žπ‘– Generalized Birecurrent Finsler Space, Journal of the Faculties of Education, University of Aden (Aden) (Yemen) (11) (2010) 21-32.
  • W. H. A. Hadi, Study of Certain Generalized Birecurrent in Finsler Space, PhD Dissertation, University of Aden (2016) Aden, Yemen.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Study Generalized ℬ𝑅-recurrent Finsler Space, International Journal of Mathematics and its Applications 4(2-B) (2016) 113-121.
  • F. Y. A. Qasem, A. A. M. Saleem, On Generalized ℬ𝑁-recurrent Finsler Space, Electronic Aden University Journal 7 (2017) 9-18.
  • A. A. A. Abdallah, On Generalized ℬ𝑅-recurrent Finsler Space, Master Thesis, University of Aden, (2017) Aden, Yemen.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Certain Generalized ℬ𝑅-recurrent Finsler Space, International Journal of Applied Science and Mathematics, 3(3) (2016) 111-114.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Generalized ℬ𝑅-recurrent Finsler Space, Electronic Aden University Journal (6) (2017) 27-33.
  • F. Y. A. Qasem, S. M. S. Baleedi, On A Generalized ℬ𝐾-recurrent Finsler Space, International Journal of Science: Basic and Applied Research 28(3) (2016) 195-203.
  • S. M. S. Baleedi, On Certain Generalized ℬ𝐾-recurrent Finsler Space, Master Thesis, University of Aden (2017) Aden, Yemen.
  • H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, Berlin GΓΆttingen- Heidelberg, (1959), 2nd Edit. (in Russian), Nauka, Moscow (1981).
  • F. Y. A. Qasem, On Generalized H-birecurrent Finsler Space, International Journal of Mathematics and its Applications 4(2-B) (2016) 51-57.
  • F. Y. A. Qasem, A. M. A. Al-qashbari, M. M. Q. Husien, On Study Generalized Rh-trirecurrent Affinely Connected Space, Journal of Scientific and Engineering Research 6(11) (2019) 179-186.
Year 2020, Issue: 32, 30 - 39, 30.09.2020

Abstract

References

  • P. N. Pandey, S. Saxena, A. Goswani, On A Generalized H-recurrent Space, Journal of International Academy of Physical Sciences 15 (2011) 201-211.
  • Z. Ahsan, M. Ali, On Some Properties of W-curvature Tensor, Palestine Journal of Mathematics, Palestine 3(1) (2014) 61-69.
  • F. Y. A. Qasem, On Transformation in Finsler Spaces, D. Phil Thesis, University of Allahabad, (Allahabad) (India) (2000).
  • M. Matsumoto, On h-isotropic and Ch-recurrent Finsler, Journal of Mathematics of Kyoto University 11 (1971), 1- 9.
  • F. Y. A. Qasem, A. A. M. Saleem, On π‘Šπ‘—π‘˜β„Žπ‘– Generalized Birecurrent Finsler Space, Journal of the Faculties of Education, University of Aden (Aden) (Yemen) (11) (2010) 21-32.
  • W. H. A. Hadi, Study of Certain Generalized Birecurrent in Finsler Space, PhD Dissertation, University of Aden (2016) Aden, Yemen.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Study Generalized ℬ𝑅-recurrent Finsler Space, International Journal of Mathematics and its Applications 4(2-B) (2016) 113-121.
  • F. Y. A. Qasem, A. A. M. Saleem, On Generalized ℬ𝑁-recurrent Finsler Space, Electronic Aden University Journal 7 (2017) 9-18.
  • A. A. A. Abdallah, On Generalized ℬ𝑅-recurrent Finsler Space, Master Thesis, University of Aden, (2017) Aden, Yemen.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Certain Generalized ℬ𝑅-recurrent Finsler Space, International Journal of Applied Science and Mathematics, 3(3) (2016) 111-114.
  • F. Y. A. Qasem, A. A. A. Abdallah, On Generalized ℬ𝑅-recurrent Finsler Space, Electronic Aden University Journal (6) (2017) 27-33.
  • F. Y. A. Qasem, S. M. S. Baleedi, On A Generalized ℬ𝐾-recurrent Finsler Space, International Journal of Science: Basic and Applied Research 28(3) (2016) 195-203.
  • S. M. S. Baleedi, On Certain Generalized ℬ𝐾-recurrent Finsler Space, Master Thesis, University of Aden (2017) Aden, Yemen.
  • H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, Berlin GΓΆttingen- Heidelberg, (1959), 2nd Edit. (in Russian), Nauka, Moscow (1981).
  • F. Y. A. Qasem, On Generalized H-birecurrent Finsler Space, International Journal of Mathematics and its Applications 4(2-B) (2016) 51-57.
  • F. Y. A. Qasem, A. M. A. Al-qashbari, M. M. Q. Husien, On Study Generalized Rh-trirecurrent Affinely Connected Space, Journal of Scientific and Engineering Research 6(11) (2019) 179-186.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Adel Mohammed Ali Al-qashbari This is me 0000-0002-4045-4520

Publication Date September 30, 2020
Submission Date October 28, 2019
Published in Issue Year 2020 Issue: 32

Cite

APA Al-qashbari, A. M. A. (2020). Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. Journal of New Theory(32), 30-39.
AMA Al-qashbari AMA. Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. JNT. September 2020;(32):30-39.
Chicago Al-qashbari, Adel Mohammed Ali. β€œSome Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space”. Journal of New Theory, no. 32 (September 2020): 30-39.
EndNote Al-qashbari AMA (September 1, 2020) Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. Journal of New Theory 32 30–39.
IEEE A. M. A. Al-qashbari, β€œSome Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space”, JNT, no. 32, pp. 30–39, September 2020.
ISNAD Al-qashbari, Adel Mohammed Ali. β€œSome Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space”. Journal of New Theory 32 (September 2020), 30-39.
JAMA Al-qashbari AMA. Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. JNT. 2020;:30–39.
MLA Al-qashbari, Adel Mohammed Ali. β€œSome Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space”. Journal of New Theory, no. 32, 2020, pp. 30-39.
Vancouver Al-qashbari AMA. Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space. JNT. 2020(32):30-9.


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