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Soleiman, Amr, Elgendi, Salah, Abdelsalam, Amani. (1399). A new general Finsler connection. سامانه مدیریت نشریات علمی, 1(1), 1-14. doi: 10.22098/jfga.2020.1002
Amr Soleiman; Salah Elgendi; Amani Abdelsalam. "A new general Finsler connection". سامانه مدیریت نشریات علمی, 1, 1, 1399, 1-14. doi: 10.22098/jfga.2020.1002
Soleiman, Amr, Elgendi, Salah, Abdelsalam, Amani. (1399). 'A new general Finsler connection', سامانه مدیریت نشریات علمی, 1(1), pp. 1-14. doi: 10.22098/jfga.2020.1002
Soleiman, Amr, Elgendi, Salah, Abdelsalam, Amani. A new general Finsler connection. سامانه مدیریت نشریات علمی, 1399; 1(1): 1-14. doi: 10.22098/jfga.2020.1002

A new general Finsler connection

Journal of Finsler Geometry and its Applications
مقاله 1، دوره 1، شماره 1، مهر 2020، صفحه 1-14    اصل مقاله (307.44 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2020.1002
نویسندگان
Amr Soleiman* 1؛ Salah Elgendi2؛ Amani Abdelsalam3
1Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. E-mail: amrsoleiman@yahoo.com
2Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. Email: alahelgendi@yahoo.com
3Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mail: a.m.abdelsalam@fsc.bu.edu.eg
چکیده
The theory of connections is an important field of research in differential geometry. It was initially developed to solve pure geometrical problems. In the Riemannian contex, M. M. Tripathi introduced a new linear connection on a Riemannian manifold, which generalizes many Riemannian connections such as symmetric, semi-symmetric, qurter-symmetric; Ricci qurter-symmetric; metric, non-metric and recurrent connections. In this paper, we extend the work of M. M. Tripath from Riemannian geometry to Finsler geometry, precisely, we investigate a new linear Finsler connection, which unifies the well known linear connections and provides new connections in Finsler geometry. This connection will be named general linear Finsler (GF-) connection. The existence and uniqueness of such a connection is proved. The curvature and torsion tensors are computed. A general reformulation for Cartan, Berwald, Chern and Hashiguchi connections is obtained. Various special cases and connections are studied and introduced. Moreover, some examples of this connection are studied.
کلیدواژه‌ها
Barthel connection؛ general Cartan connection؛ general Berwlad connection؛ general Hashiguchi connection؛ general Chern(Rund) connection
مراجع
  • 1. N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifolds, Indian J. Pure Appl. Math., 23 (1992), 399-409.
  • 2. O. C. Andonie and D. Smaranda, Certaines connexions semi-sym`etriques, Tensor, N. S.,
    31 (1977), 8-12.
  • 3. E. Cartan, Les espaces de Finsler, Actualities 79, Paris, 1934.
  • 4. D. Bao, S. S. Chern, and Z. Shen, An introuduction to Riemann-Finsler geometry,
    Springer-Verlag, Berlin, 2000.
  • 5. G. B. Folland, Weyl manifolds, J. Diff. Geom., 4 (1924), 145-153.
  • 6. Y. Liang, On semi-symmetric recurrent-metric connection, Tensor, N. S., 55 (1994),
    107-112.
  • 7. M. Matsumoto, Finsler connections with many torsions, Tensor, N. S., 17 (1966), 217-
    226.
  • 8. M. Matsumoto, The theory of Finsler connections, Publication of the study group of
    geometry, Vol. 5, Dept. Math., Okayama Univ., 1970.
  • 9. M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha
    Press, Japan, 1986.
  • 10. R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connections, Tensor, N.
    S., 34 (1980), 1-7.
  • 11. B. N. Prasad, H.S. Shukla and D.D.Singh, On recurrent Finsler connections with deflection and torsion, Pub. Math. Debrecen, 35 (1988), 77-84.
  • 12. B. N. Prasad and L. Srivastava, On hv-recurrent Finsler connection, Indian J. Pure
    Appl. Math., 20 (1989), 790-798.
  • 13. H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.
  • 14. J. Sengupta, U. C. De and T. Q. Binh, On a type of semi-symmetric non-metric connection on Riemannian manifolds, Indian J. Pure Appl. Math., 31 (2000), 1659-1670.
  • 15. A. Soleiman, Global theory of vertical recurrent Finsler connection, Submitted.
  • 16. J. Szilasi and C. Vincze, A new look at Finsler connections and special Finsler manifolds,
    Acta Math. Acad. Paedagog. Nyh´azi., N. S., 16 (2000), 33–63.
  • 17. J. Szilasi, R.L. Lovas, D.Cs. Kert´esz,v Connections, Sprays and Finsler Structures, World
    Scientific, 2014.
  • 18. A. A. Tamim and S. H. Abed, Semi-symmetric metric connection in Finsler geometry,
    J.Egypt. Math. Soc., 11(2) (2003), 61-72.
  • 19. M. M. Tripathi, A new connection in a Riemannian manifold, Int. Electron. J. Geom.,
    1 (2008), 15-24.
  • 20. V. Wagner, Theory of field of local (2n-2) dimensional surface in Xn and its applications
    to the problem of Lagrange in the calculus of variations, Ann. Math., 49(2) (1948), 141-
    188.
  • 21. K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl.,
    15 (1970), 1579-1586.
  • 22. K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker Inc., 1970.
  • 23. K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors,
    Tensor, N. S., 38 (1984), 13-18.
  • 24. Nabil L. Youssef, Connexions me´triques semi-syme´trique semi-basiques, Tensor, N.
    S.,40(1983), 242-248.
  • 25. Nabil L. Youssef, Vertical semi-symmetric metric connection, Tensor, N. S.,49(1990),
    218-229.
  • 26. Nabil L. Youssef, S. H. Abed and A. Soleiman, Cartan and Berwald connections in
    the pullback formalism, Algebras, Groups and Geometries, 25 (2008), 363-384. arXiv:
    0707.1320 [math. DG].
  • 27. 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. arXiv: 0801.3220
    [math.DG].
  • 28. Nabil L. Youssef and A. Soleiman, On horizontal recurrent Finsler connection, Rend.
    Circ. Mat. Palermo, II. Ser 2, 68 (2019), 1-9. 
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