New special Finsler spaces

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

2 Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza, Egypt.

Abstract

The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations between them are singled out.

Keywords

References

  • 1. H. Akbar-Zadeh, Initiation to global Finsler geometry, Elsevier, 2006.
  • 2. J. Grifone, Structure pr´esque-tangente et connexions, I, Ann. Inst. Fourier, Grenoble,
    22, 1 (1972), 287-334.
  • 3. U. C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor,
    N. S., 56 (1995), 312-317.
  • 4. Y. B. Maralabhavi and M. Rathnamma, On generalized recurrent manifold, Indian J.
    Pure Appl. Math., 30 (1999), 1167-1171.
  • 5. M. Matsumoto, On h-isotropic and Ch-recurrent Finsler spaces, J. Math. Kyoto Univ.,
    11 (1971), 1-9.
  • 6. R. S. Mishra and H. D. Pande, Recurrent Finsler spaces, J. Ind. Math. Soc., 32 (1968),
    17-22.
  • 7. R. H. Ojha, m-projectvely flat Saskian manifold, Indian J. Pure Appl. Math., 4 (1985),
    481- 484.
  • 8. E. M. Patterson, Some theorems on Ricci recurrent spaces, J. London Math. Soc., 27
    (1952), 287-295.
  • 9. S. K. Saha, On Type of Riemannian manifold, Bull. Cal. Math. Soc., 101 (2009), 553-558.
  • 10. J. P. Singh, On an Einstein m-projectve P-Sasakian amnifolds, Bull. Cal. Math. Soc.,
    101 (2009), 175-180.
  • 11. H. Singh and Q. Khan, On generalized recurrent Riemannian manifolds, Publ. Math.
    Debrecen, 56 (2000), 87-95.
  • 12. A. G. Walker, On Ruses’s spaces of recurrent curvature, Proc. London Math. Soc., 52
    (1950), 36-64.
  • 13. Nabil L. Youssef and A. Soleiman, On concircularly recurrent Finsler manifolds, Balkan
    J. Geom. Appl., 18 (2013), 101-113.
  • 14. Nabil L. Youssef and A. Soleiman, Some types of recurrence in Finsler geometry, submitted. arXiv: 1607.07468v2 [math.DG].
  • 15. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of special
    Finsler manifolds, J. Math. Kyoto Univ., 48 (2008), 857-893.
  • 16. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global theory of conformal Finsler
    geometry, Tensor, N. S., 69 (2008), 155–178.
  • 17. Nabil L. Youssef, S. H. Abed and A. Soleiman, Cartan and Berwald connections in the
    pullback formalism, Algebras, Groups and Geometries, 25 (2008), 363–386.
  • 18. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of connections in Finsler geometry, Tensor, N. S., 71 (2009), 187-208.
  • 19. Nabil L. Youssef, S. H. Abed and A. Soleiman, Concurrent π-vector fields and eneregy
    β-change, Int. J. Geom. Meth. Mod. Phys., 6 (2009), 1003-1031.
  • 20. Nabil L. Youssef, S. H. Abed and A. Soleiman, Geometric objects associated with the
    fundumental connections in Finsler geometry, J. Egypt. Math. Soc., 18 (2010), 67-90. 
Journal of Finsler Geometry and its Applications
Volume 4, Issue 1
July 2023
Pages 114-123

Files

Share

How to cite

Statistics