On Generalized Recurrent Finsler Spaces of Higher Order with Berwald’s Curvature Tensor

DOI: https://doi.org/10.24086/cuesj.v7n2y2023.pp35-41
Keywords: Generalized BK-five-recurrent, Berwald’s derivative of fifth order, curvature tensor Ki_jkh, curvature tensor Ri_jkh, Weyl projective curvature tensor Wi_jkh

Abstract

In this present paper, we introduced a Finsler space Fn which projective curvature tensor K^i_ijkh satisfies the generalized five recurrence property with respect to Berwald’s connection parameters G^i_kh, we have derived some theorems and some identities along with few more related results in a recurrent and generalized 5-recurrent Finsler space with Berwald’s curvature tensor field.

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Author Biographies

Salem Saleh, Department of Computer Science, Cihan University-Erbil, Kurdistan Region, Iraq, Department of Mathematics, Hodeidah University, Hodeidah, Yemen
S. Saleh is a Professor of pure Mathematics at Hodeidah University-Yemen, Currently, he is a research fellow in the Department of Computer Science at Cihan University-Erbil, Iraq. His research interests are in the areas of pure and Fuzzy mathematics including Topology, Fuzzy topology, Interval-valued fuzzy topology, Soft, fuzzy soft, neutrosophic set theory, and its applications. He has many published research articles in reputed international journals of mathematical sciences.
A. M.A. Al-Qashbari, Department of Mathematics, Faculty of Education-Aden, Aden University, Yemen

Adel M. A. Al-Qashbari is an associative Professor of pure and applied Mathematics at Aden University-Aden, Yemen, Currently, he is the head of the Mathematics Department, Faculty of Education, Aden University. His research interests are in the areas of pure and applied mathematics including Differential Geometry, Finsler spaces and its generalizations, Curvature tensor and its applications. He has a list of published papers in local and international journals of mathematics.

References

A. A. A. Abdallah, On Generalize BR-Recurrent Finsler Space, M. Sc. Dissertation. University of Aden, Aden, Yemen, 2017.

M. A. AL-Qashbari, F. Y. A. Qasem. Study on generalized Br-trirecurrent finsler space. Journal of Yemen engineer, Faculty of Engineering, University of Aden, vol. 15, pp. 79-89, 2017.

H. Rund. The Differential Geometry of Finsler Spaces, Springer- Verlag, Berlin, 1959, 2nd ed., Nauka, Moscow, 1981.

M. A. AL-Qashbari. On generalized for curvature tensors of second order in finsler space. University of Aden Journal of Natural and Applied Sciences, vol. 24, no.1, pp. 171-176, 2020.

Z. Ahsan and M. Ali. On some properties of w-curvature tensor. Palestine Journal of Mathematics, Palestine, vol. 3, no. 1, pp. 61-69, 2014.

H. Abu-Donia, S. Shenawy and A. Abdehameed, The w-curvature tensor on relativistic space-times. Kyungpook Mathematical Journal, vol. 60, pp. 185-195, 2020.

M. A. AL-Qashbari. Some properties for weyl’s projectiv curvature tensor of generalized Wh-birecurrent in finsler space. University of Aden Journal of Natural and Applied Sciences, vol. 23,no. 1, pp. 181-189, 2019.

M. H. Emamian and A. Tayebi. Generalized douglas-weyl finsler metrics. Iranian Journal of Mathematical Sciences and Informatics, vol. 10, no. 2, pp. 67-75, 2015.

H. M. Awed. On Study of Generalized Recurrent Finsler Spaces, M.Sc. Dissertation. University of Aden, Yemen, 2017.

S. M. S. Baleedi. On Certain Generalized. BK-Recurrent Finsler Space, M. Sc. Dissertation. University of Aden, Aden, Yemen, 2017.

M. A. H. Al-Qufail. Decomposability of curvature tensors in non-symmetric recurrent finsler space. Imperial Journal of Interdisciplinary Research, vol. 3, no. 2, pp. 198-201, 2017.

P. N. Pandey, S. Saxena and A. Goswani. On a generalized H-recurrent space. Journal of International Academy of Physical Sciences, vol. 15, pp. 201-211, 2011.

B. Bidabad, M. Sepasi. Complete finsler spaces of constant negative Ricci curvature. Journal of Mathematics Differential Geometry, vol. 1, 19, pp. 1-12, 2020.

B. Misra, S. B. Misra, K. Srivastava and R. B. Srivastava. Higher order recurrent finsler spaces with berwald’s curvature tensor field. Journal of Chemical, Biological and Physical Sciences, vol. 4, no. 1, pp. 624-631, 2014.

M. A. AL-Qashbari. Some identities for generalized curvature tensors in B-recurrent finsler space. Journal of New Theory, vol. 32, pp. 30-39, 2020.

Goswami. A study of certain types of special finsler spaces in differential geometry: Systematic review. Mathematics Applied in Science and Technology, vol. 9, no. 1, p. 23-30, 2017.

W. H. A. Hadi. Study of Certain Generalized Birecurrent in Finsler Space, Ph. D. Thesis. University of Aden, Yemen, 2016.

H. D. Pandey and S. D. Tripathi. W-third order recurrent finsler space. İstanbul Üniversitesi Fen Fakültesi Series A, vol. 46-47, pp. 61-66, 1981-1982.

F. Y. A. Qasem. On generalized H-birecurrent finsler space. International journal of Mathematics and Its Applications, vol. 4, no. 2-B, pp. 51-57, 2016.

M. A. AL-Qashbari. Recurrence decompositions in finsler space. Journal of Mathematical Analysis and Modelling, vol. 1, pp. 77-86, 2020.

F. Y. A. Qasem and A. A. A. Abdallah. On generalized BR-recurrent finsler space. Electronic Aden University Journal, vol. 21, no. 6, pp. 27-33, 2017.

F. Y. A. Qasem and A. A. A. Abdallah. On certain generalized BR-recurrent finsler space. International Journal of Applied Science and Mathematics, vol. 3, no. 3, pp. 111-114, 2016.

F. Y. A. Qasem and A. A. A. Abdallah. On study generalized BR-recurrent finsler space. International Journal of Mathematics and its Applications, vol. 4, no. 2-B, pp. 113-121, 2016.

F. Y. A. Qasem, A. M. A. Al-Qashbari and M. M. Q. Husien. On study generalized Rh-trirecurrent affinely connected space. Journal of Scientific and Engineering Research, vol. 6, no. 1, pp. 179-186, 2019.

F. Y. A. Qasem and S. M. S. Baleedi. On a generalized BK-recurrent finsler space. International Journal of Science Basic and Applied Research, vol. 28, no. 3, pp. 195-203, 2016.

F. Y. A. Qasem and A. A. M. Saleem. On generalized birecurrent finsler space. Journal of the Faculties of Education, University of Aden, vol. 14, no. 11, pp. 21-32, 2010.

Z. Ahsan and M. Ali. Curvature tensor for the spacetime of general relativity. Palestine Journal of Mathematics, vol. 2, no. 28, pp. 1-15, 2016.

Published
2023-09-20
How to Cite
1.
Saleh S, Al-Qashbari A. On Generalized Recurrent Finsler Spaces of Higher Order with Berwald’s Curvature Tensor. cuesj [Internet]. 20Sep.2023 [cited 18May2024];7(2):35-1. Available from: https://journals.cihanuniversity.edu.iq/index.php/cuesj/article/view/995
Issue
Vol 7 No 2 (2023)
Section
Research Article

Copyright (c) 2023 Salem Saleh, A. M.A. Al-Qashbari

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