Diverse forms of generalized birecurrent Finsler space

Document Type : Original Article

Authors

1 Department of Mathematics, Hamedan Branch, Islamic Azad University,Hamedan, Iran

2 Department of Mathematics, Abyan University, Abyan, Yemen.

3 Department of Mathematics, Pratishthan Mahavidyalaya, Paithan, India.

4 Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.

5 Department of Mathematics, Taiz University, Taiz P.O. Box 6803, Yemen

Abstract

The generalized birecurrent Finsler space have been introduced by the Finslerian geometers. The purpose of the present paper is to study three special form of Pijkh in generalized BP􀀀birecurrent space. Weu se the properties of P2-like space, P-space and P-reducible space in the main space to get new spaces that will be called a P2-like generalized BP-recurrent space, P-generalized BP􀀀birecurrent space and P-reducible generalized BP􀀀birecurrent space, respectively. In addition, we prove that the Cartan's firrst curvature tensor Sijkh satisfies the birecurrence property. Certain identities belong to these spaces have been obtained. Further, we end up this paper with some demonstrative examples.

Keywords

References

  • 1. A.A. Abdallah, A.A. Hamoud, A. Navlekar, K. Ghadle, B. Hardan, H. Emadifar, and
    M. Khadem, On Birecurrent for Some Tensors in Various Finsler Spaces, Journal of
    Finsler Geometry and its Applications, 4(1)(2023), 33-44.
  • 2. A.A. Abdallah, A.A. Navlekar, K.P. Ghadle, and B. Hardan, Fundamentals and recent
    studies of finsler geometry, International Journal of Advances in Applied Mathematics
    and Mechanics, 10(2)(2022), 27-38.
  • 3. A.A. Abdallah, A.A. Navlekar, and K.P. Ghadle, On B−covariant derivative of first order for some tensors in different spaces, Journal of Mathematical Analysis and Modeling, 2(2)(2021), 30-37.
  • 4. A.A. Abdallah, A.A. Navlekar, and K.P. Ghadle, Special types of generalized BP −recurrent spaces, Journal of Computer and Mathematical Sciences, 10(5)(2019), 972-979.
  • 5. A.A. Abdallah, A.A. Navlekar, K.P. Ghadle, and A.A. Hamoud, Decomposition for Cartan’s second curvature tensor of different order in Finsler spaces, Nonlinear Functional Analysis and Applications, 27(2)(2022), 433-448.
  • 6. A.M. Al-Qashbari, Recurrence decompositions in Finsler space, Journal of Mathematical
    Analysis and Modeling, 1(1)(2020), 77-86.
  • 7. F.A. Assallal, On certain generalized h−birecurrent of curvature tensor, M.Sc. Thesis,
    University of Aden, (Yemen), (2018).
  • 8. M. Dahl, An brief introduction to Finsler geometry, Springer, (2006).
  • 9. A.D. Dubey, Special Finsler spaces - a review of literature, International Journal of
    Research and Development in Applied Science and Engineering, 12(1)(2017), 6-8.
  • 10. P.K. Dwivedi, P∗−reducible Finsler spaces and applications, Int. journal of Math. Analysis, 5(5)(2011), 223-229.
    11. M. Gheorghe, The indicatrix in Finsler geometry, Analele Stiintifice Ale Uuiversitatii
    Matematica. Tomul LIII, (2007), 163-180.
  • 12. W.H. Hadi, Study of certain types of generalized birecurrent in Finsler spaces, Ph.D.
    Thesis, Faculty of Education-Aden, University of Aden, (Yemen), (2016).
  • 13. H. Izumi, On Finsler space of scalar curvature, Tensor N.S., 38(1982), 220-222.
  • 14. M. Matsumoto, On h−isotropic and Ch- recurrent Finsler, J. Math. Kyoto Univ.,
    11(1971), 1-9.
  • 15. M. Matsumoto, On Finsler spaces with curvature tensor of some special forms, Tensor
    N. S., 22(1971), 201-204.
  • 16. S.K. Narasimhamurthy, P. Kumar, and S.T. Aveesh, A study of hypersurfaces on special
    Finsler spaces, International Journal of Pure and Applied Mathematics, 48(1)(2008), 67-74.
  • 17. S.I. Ohta, Comparison Finsler geometry, Springer International Publishing, (2021).
  • 18. A.M. Otman, On covariant differentiation for curvature tensor of third order in the
    sense of Berwald, M.SC. Thesis, University of Aden, Yemen, (2018).
  • 19. F.Y. Qasem, and W.H. Hadi, On a generalized BR−birecurrent affinely connected space,
    International Journal of Mathematics and statistics invention, 4(5)(2016), 30-33.
  • 20. H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin Gttingen,
    (1959); 2nd Edit. (in Russian), Nauka, (Moscow), 1981.
  • 21. P.S. Saxena, A study of P∗−reducible Finsler space with Douglas tensor, Journal of
    International Academy of physical Science, 17(3)(2013), 277-285.
  • 22. Y.B. Shen, and S. Zhongmin, Introduction to modern Finsler geometry, World Scientific
    Publishing Company, (2016).
  • 23. B.K. Tripathi, and K.B. Pandey, On a special form of h(hv)−torsion tensor Pijk in
    Finsler space, Journal of Mathematics, Hindawi, (2016), 1-5.
  • 24. H. Wosoughi, On P3−Like Finsler spaces, Journal of Mathematics and Statistics Research, 2(1)(2020), 1-2.
  • 25. S.M. Zamanzadeh, B. Najafi, and M. Toomanian, On generalized P −reducible Finsler
    manifolds, Open Mathematics Research Article, 16(2018), 718-723.
Journal of Finsler Geometry and its Applications
Volume 4, Issue 1
July 2023
Pages 88-101

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