Browse > Article
http://dx.doi.org/10.4134/CKMS.c200232

GLOBAL THEORY OF VERTICAL RECURRENT FINSLER CONNECTION  

Soleiman, Amr (Department of Mathematics College of Science and Arts Al Jouf University and Department of Mathematics Faculty of Science Benha University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.3, 2021 , pp. 593-607 More about this Journal
Abstract
The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.
Keywords
Finsler manifold; Barthel connection; Cartan connection; Berwald connection; vertical recurrent Finsler connection;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. N. Prasad and L. Srivastava, On hv-recurrent Finsler connection, Indian J. Pure Appl. Math. 20 (1989), no. 8, 790-798.
2 J. Szilasi, R. L. Lovas, and D. Cs. Kertesz, Connections, Sprays and Finsler Structures, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2014.
3 A. A. Tamim, General theory of Finsler spaces with applications to Randers spaces, Ph. D. Thesis, Cairo University, 1991.
4 N. L. Youssef, Sur les tenseurs de courbure de la connexion de Berwald et ses distributions de nullite, Tensor (N.S.) 36 (1982), no. 3, 275-280.
5 N. L. Youssef, S. H. Abed, and A. Soleiman, Cartan and Berwald connections in the pullback formalism, Algebras Groups Geom. 25 (2008), no. 4, 363-384.
6 N. L. Youssef, S. H. Abed, and A. Soleiman, A global approach to the theory of special Finsler manifolds, J. Math. Kyoto Univ. 48 (2008), no. 4, 857-893.
7 N. L. Youssef, S. H. Abed, and A. Soleiman, A global approach to the theory of connections in Finsler geometry, Tensor (N.S.) 71 (2009), no. 3, 187-208.
8 N. L. Youssef, S. H. Abed, and A. Soleiman, Geometric objects associated with the fundamental connections in Finsler geometry, J. Egyptian Math. Soc. 18 (2010), no. 1, 67-90. https://doi.org/10.1215/kjm/1250271321   DOI
9 N. L. Youssef and A. Soleiman, On horizontal recurrent Finsler connections, Rend. Circ. Mat. Palermo (2) 68 (2019), no. 1, 1-9. https://doi.org/10.1007/s12215-018-0336-z   DOI
10 H. Akbar-Zadeh, Initiation to global Finslerian geometry, North-Holland Mathematical Library, 68, Elsevier Science B.V., Amsterdam, 2006.
11 D. Bao, S.-S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, Graduate Texts in Mathematics, 200, Springer-Verlag, New York, 2000. https://doi.org/10.1007/978-1-4612-1268-3
12 P. Dazord, Proprietes globales des geodesiques des espaces de Finsler, These d'Etat, (575) Publ. Dept. Math. Lyon, 1969.
13 J. Grifone, Structure presque-tangente et connexions. I, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 1, 287-334.   DOI
14 J. Grifone, Structure presque-tangente et connexions. II, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 291-338. (loose errata).   DOI
15 F. Ikeda, On S3- and S4-like Finsler spaces with the T-tensor of a special form, Tensor (N.S.) 35 (1981), no. 3, 345-351.
16 A. Soleiman, Recurrent Finsler manifolds under projective change, Int. J. Geom. Methods Mod. Phys. 13 (2016), no. 10, 1650126, 10 pp. https://doi.org/10.1142/S0219887816501267   DOI
17 J. Klein and A. Voutier, Formes exterieures generatrices de sprays, Ann. Inst. Fourier (Grenoble) 18 (1968), fasc. 1, 241-260.   DOI
18 R. Miron and M. Anastasiei, The geometry of Lagrange spaces: theory and applications, Fundamental Theories of Physics, 59, Kluwer Academic Publishers Group, Dordrecht, 1994. https://doi.org/10.1007/978-94-011-0788-4