Some Identities for Generalized Curvature Tensors in 𝓑-Recurrent Finsler Space
Yıl 2020,
Sayı: 32, 30 - 39, 30.09.2020
Adel Mohammed Ali Al-qashbari
Öz
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 𝑃𝑗𝑘ℎ𝑖 satisfies the generalized of recurrence condition with respect to Berwald’s connection parameters G𝑘ℎ𝑖 which given by the condition ℬ𝑚𝑃𝑗𝑘ℎ𝑖=𝜆𝑚 𝑃𝑗𝑘ℎ𝑖+𝜇𝑚( 𝛿ℎ𝑖 𝑔𝑗𝑘− 𝛿𝑘𝑖 𝑔𝑗ℎ), where ℬ𝑚 is covariant derivative of first order (Berwald’s covariant differential operator ) with respect to 𝑥𝑚, 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 𝑃𝑘ℎ 𝑖, the deviation tensor 𝑃ℎ 𝑖 and the covariant derivative of the tensor 𝐻𝑘𝑝.ℎ (in the sense of Berwald), also we find some theorems of the R-Ricci tensor 𝑅𝑗𝑘 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 𝑊𝑗𝑘ℎ𝑖 and its torsion tensor 𝑊𝑘ℎ𝑖 in our space. Also, we have proved that in 𝐺ℬ𝑃-𝑅𝐹𝑛, Cartan’s second curvature tensor 𝑃𝑗𝑘ℎ𝑖 and the v(hv)-torsion tensor 𝑃𝑘ℎ𝑖 for 𝑛=4 .
Destekleyen Kurum
Department of Mathematics, Faculty of Education -Aden, University of Aden.
Kaynakça
- 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 𝑊𝑗𝑘ℎ𝑖 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 Göttingen- 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.
Yıl 2020,
Sayı: 32, 30 - 39, 30.09.2020
Adel Mohammed Ali Al-qashbari
Kaynakça
- 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 𝑊𝑗𝑘ℎ𝑖 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 Göttingen- 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.