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On the L-duality of a Finsler space with special (α, β) metric | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 1، شهریور 2023، صفحه 173-182 اصل مقاله (313.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2520 | ||
| نویسندگان | ||
| Brijesh Kumar Tripathi* 1؛ Manoj Kumar Singh2 | ||
| 1Department of Mathematics, L. D. College of Engineering, Ahmedabad, Gujarat-380015, India. | ||
| 2Department of Mathematics, Government Engineering College-Dahod, Gujarat-389151, India. | ||
| چکیده | ||
| R. Miron initiated the study of L-duality in Lagrange and Finsler spaces in 1987.The concrete L-duals of the Randers met-ric, Kropina metric, Matsumoto metric, exponential metric, as well as a few more unique (α, β)- metrics, are really just an of the re-markable results obtained.The importance of L-duality, however, is basically limited to finding the dual of a few key Finsler functions.In this paper, we find L- Dual of a Finsler space with a special (α, β)- metric F =(α+β)3/α2 , where α is a Riemannian metric and β is a differential one form. | ||
| کلیدواژه‌ها | ||
| Finsler Space؛ Cartan space؛ L- Dulity between Finsler and Cartan Spaces | ||
| مراجع | ||
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[1] Brijesh Kumar Tripathi, Nonholonomic Frames for Finsler Space with Deformed Special (α, β)-Metric, International Journal of Mathematical Combinatorics, 1 (2018), 61-67. [2] Brijesh Kumar Tripathi and V. K. Chaubey, Deformed Infinite Series Metric in Cartan Spaces, Palestine Journal of Mathematics, 11(3) (2022), 194-204. [3] D. Hrimiuc and H. Shimada, On the L-duality between Lagrange and Hamilton manifolds, Nonlinear World, 3 (1996), 613-641. [4] D. Hrimiuc and H. Shimada, On some special problems concerning the L-duality between Finsler and Cartan spaces, Tensor, N.S., 58 (1) (1997), 48-61. [5] I. M. Masca, S. V. Sabau and H. Shimada, The L- Duality of a Matsumoto space, Publ Math. Debrecen,72(2008),272-242. [6] M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaisheisha Press, Otsu, Japan, (1986). [7] M. Matsumoto, Finsler Geometry in the 20th- century, In: Handbook of Finsler Geometry, Vol. I, II(Ed. by P. L. Antonelli) Kulwer Acad. Publ. (2003), 557-966. [8] P. L. Antonelli, Hand Book of Finsler Geometry, Kulwer Acad. Publ. FTPH, 58(1993). [9] R. Miron, Cartan spaces in a new point of view by considering them as duals of Finsler spaces, Tensor, N.S., 46 (1987), 330-334. [10] R. Miron, The Geometry of Higher-order Lagrange Spaces, Applications to Me-chanics and Physics, Kulwer Acad. Publ. FTPH, 82 (1997). [11] R. Miron, The Geometry of Higher-order Hamilton Spaces, Applications to Hamiltonian Mechanics, Kulwer Acad. Publ. FTPH, 132 (2003). [12] R. Miron, The Geometry of Higher-order Finsler Spaces, Applications to Hamil-tonian Mechanics Hadronic Press., Inc., USA, (1998). [13] R. Miron and M. Anastasiei, The Geometry of Lagrange Spaces, Theory and Applications, Kulwer Acad. Publ. FTPH, 59 (1994). [14] R. Miron, D. Hrimiuc, H. Shimada and S. V. Sabau, The Geometry of Hamil-tonian and Lagrange Spaces, Kulwer Acad. Publ. FTPH, 118 (2001). [15] R. S. Kushwaha and G. Shanker, On the L-duality of a Finsler space with ex-ponential metric α.eβ/α , Acta Univ. Sapientiae, Mathematica, 10(1) (2018), 167-177. [16] S. V. Sabau, and H. Shimada, Classes of Finsler spaces with (α, β)- metrics,Rep. on Math. Phys., 47 (2001), 31-48. [17] Z. Shen, On Landsberg (α, β)-metrics, http: www.math.iupiu.edu/ zshen /Re-search/papers, (2006). | ||
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