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MECHANICAL SYSTEMS ON AN ALMOST KÄHLER MODEL OF A FINSLER MANIFOLD

Department of Econometrics, Çanakkale Onsekiz Mart University, Faculty of Economics and Administrative Sciences at Biga, 17020 Biga/Çanakkale, Turkey

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OGUZHAN CELIK

Çanakkale Onsekiz Mart University, Institue of Naturel and Applied Sciences, 17020 Çanakkale, Turkey

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https://doi.org/10.1142/S0219887813200181Cited by:0 (Source: Crossref)

Abstract

In this study, we present a new analogue of Euler–Lagrange and Hamilton equations on an almost Kähler model of a Finsler manifold. Also, we give some corollaries about the related mechanical systems and equations.

Keywords:

AMSC: 53C15, 70H03, 70H05

References

M. De Leon and P. R. Rodrigues , Methods of Differential Geometry in Analytical Mechanics , North-Holland Mathematics Studies 152 ( Elsevier , Amsterdam , 1989 ) . Google Scholar
M. Matsumoto , Foundations of Finsler Geometry and Special Finsler Spaces ( Kaisisha, Shingaken , Japan , 1986 ) . Google Scholar
J. Kern , Archiv der Mathematik (Basel) 25 , 438 ( 1974 ) . Crossref, Web of Science, Google Scholar
V. Oproiu, Some properties of the tangent bundle related to the Finsler geometry, Proc. Nat. Sem. Finsler Spaces (Brasov, 1980) pp. 195–207. Google Scholar
V. Oproiu, Rend. Sem. Fac. Sci. Univ. Cagliari 55(2), 1 (1985). Google Scholar
D. Baleanu and S. I. Vacaru, Fractional almost Kähler–Lagrange geometry, [math-ph] , arXiv: 1006.5535v3 . Google Scholar
S. I. Vacaru, Lagrange–Ricci flows and evolution of geometric mechanics and analogous gravity on Lie algebroids, [math-ph] , arXiv: 1108.4333v2 . Google Scholar
S. I. Vacaru, Finsler and Lagrange geometries in Einstein and string gravity, [gr-qc] , arXiv: 0801.4958v1 . Google Scholar
R. Miron et al. , The Geometry of Hamilton and Lagrange Spaces ( Kluwer Academic Publishers , Hingham, MA, USA , 2001 ) . Google Scholar
P. L. Antonelli and R. Miron , Lagrange and Finsler Geometry Applications to Physics and Biology 76 ( Kluwer Academic Publishers , 1996 ) . Crossref, Google Scholar
R. Miron and M. Anastasiei , Vector Bundles. Lagrange Spaces. Applications to the Theory of Relativity ( Balkan Press , Bucuresti , 1997 ) . Google Scholar
C. Udrişte and M. Neagu, Diff. Geom. Dynam. Syst. 1(1), 10 (1999). Google Scholar
M. Tekkoyun , Phys. Lett. A 340 , 7 ( 2005 ) . Crossref, Web of Science, Google Scholar
M. Tekkoyun and Y. Yayli, Int. J. Geom. Meth. Mod. Phys. 8(7), 1419 (2011). Link, Web of Science, Google Scholar
V. Oproiu, Int. J. Math. Math. Sci. 25(3), 183 (2001). Crossref, Google Scholar