Lagrange spaces with changed (α, β)− metric with Shen’s square Randers metric

Document Type : Original Article

Authors

1 Department of Mathematics K.S.Saket P.G. College, Ayodhya, India

2 Adarsh inter college Saltauwa, India

Abstract

The aim of the present paper is to study the Lagrange spaces due to changed (α,β)-metric with Z. Shen square- Randers metric L ̅= 〖(α+β)〗^2/α+ β and obtained fundamental tensor fields for these space. Further, we studied about the variational problem with fixed endpoints for the Lagrange spaces due to above change.

Keywords


 1. B. Nicolaescu, Lagrange spaces with (α; β) - metric, A ppl. Sci.,3 :1 , 3(2001).
2. B. Nicolaescu,
The variational problem in Lagrange spaces endowed with (α; β)- metric,in Balan, Vladimir (ed.),Proceedings of the 3rd international colloquium of Mathematics in engineering and numericalphysics (MENP -3) Bucharest, Romania, (2004), Mathematics sections, BSG proceedings, 12, Geometry Balken Press, Bucharest, (2005), 202 - 207.
3. C. Shibata,
On invariant tensors of β- changes of Finsler metrics, J. Math. kyoto Univ.,24(1984), 163-188.
4. J. Kern,
Lagrange geometry, Arch Math., 25(1974), 438-443.
5. I.M.Gelfand, S.V. Fomin,
Calculus of variations, Dover publications, Mineola,(2000).
6. M. Matsumoto ,
On some transformations of locally Minkowskian space, Tensor. N. S.22(1971), 103-111.
7. M. Matsumoto ,
Theory of Finsler spaces with (α; β)- metric, Rep. Math. Phys.,31:1(1992).
8. R. Miron, A Lagrangian theory of relativity, I,II, An. stiint . Univ. AI.I. cuza Iasi, N. S.,sect. Ia,32 : 2,3, 37-62, 7 -16 (1986).
9. R. Miron,
Lagrange geometry, Math. Comput. Modelling, 20(1994), 4-5, 25-40.
10. R. Miron, M. Anastasiei,
The geometry of Lagrange spaces : theory and applications,Kluwer Acad. Publ., Dordrecht, (1994).
11. S.S.Chern, Z. Shen,
Riemann - Finsler geometry, Nankai Tracts in Mathematics, World Scientific, Hackensack, 06(2005).
12. T. N. Pandey, V. K. Chaubey,
Lagrange spaces with β- change, Int. J. Contemp.Math.sci. 07(2012), 45-48, 2363-2371.
13. T. N. Pandey, V. K. Chaubey,
The variational problem in Lagrange spaces endowed with (γ; β) metric, Int. J. Pure.Appl. Math., 71:4(2011), 633-638.
14. V.K.Chaubey, B.K. Tripathi, S.B.Chandak,
Lagrange spaces with change Z.shen square metric, Siberian electronic Mathematical reports, 20:1(2023), 17-24.
15. Z. Shen, G. C. Yildirim,
On a class of projectively flat metrics with constant flag curvature, can. J. Math., 60:2(2008), 443-456.