Geodesic
Lagrange spaces with changed Z. Shen square metric
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 17-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of present paper to study Lagrange space due to changed Z. Shen square metric $L^{*}=\frac{(L+\beta)^{2}}{L}$ 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: Z. Shen square metric
Mots-clés : Lagrange space, Euler-Lagrange equation. 
@article{SEMR_2023_20_1_a15,
     author = {Kumar Tripathi Brijesh and S. B. Chandak and V. K. Chaubey},
     title = {Lagrange spaces with changed {Z.} {Shen} square metric},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {17--24},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a15/}
}
TY  - JOUR
AU  - Kumar Tripathi Brijesh
AU  - S. B. Chandak
AU  - V. K. Chaubey
TI  - Lagrange spaces with changed Z. Shen square metric
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 17
EP  - 24
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a15/
LA  - en
ID  - SEMR_2023_20_1_a15
ER  - 
%0 Journal Article
%A Kumar Tripathi Brijesh
%A S. B. Chandak
%A V. K. Chaubey
%T Lagrange spaces with changed Z. Shen square metric
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 17-24
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a15/
%G en
%F SEMR_2023_20_1_a15
Kumar Tripathi Brijesh; S. B. Chandak; V. K. Chaubey. Lagrange spaces with changed Z. Shen square metric. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 17-24. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a15/

[1] B. Nicolaescu, “Lagrange spaces with $ (\alpha, \beta) $-metric”, Appl. Sci., 3:1 (2001), 42–47 | MR | Zbl

[2] B. Nicolaescu, “The variational problem in Lagrange spaces endowed with $ (\alpha, \beta) $-metric”, Proceedings of the 3rd international colloquium of mathematics in engineering and numerical physics, MENP-3, Mathematics sections (Bucharest, Romania, October 7-9, 2004), BSG Proceedings, 12, ed. Balan Vladimir, Geometry Balkan Press, Bucharest, 2005, 202–207 | MR | Zbl

[3] C. Shibata, “On invariant tensors of $ \beta $-changes of Finsler metrics”, J. Math. Kyoto Univ., 24 (1984), 163–188 | MR | Zbl

[4] J. Kern, “Lagrange geometry”, Arch. Math., 25 (1974), 438–443 | DOI | MR | Zbl

[5] I.M. Gelfand, S.V. Fomin, Calculus of variations, Dover Publications, Mineola, 2000 | MR | Zbl

[6] M. Matsumoto, “On some transformations of locally Minkowskian space”, Tensor, New Ser., 22 (1971), 103–111 | MR | Zbl

[7] M. Matsumoto, “Theory of Finsler spaces with $ (\alpha, \beta) $-metric”, Rep. Math. Phys., 31:1 (1992), 43–83 | DOI | MR | Zbl

[8] R. Miron, “A Lagrangian theory of relativity, I; II”, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, N. Ser., Secţ. Ia, 32:2 (1986), 7–16 | MR | Zbl

[9] R. Miron, “Lagrange geometry”, Math. Comput. Modelling, 20:4-5 (1994), 25–40 | DOI | MR | Zbl

[10] R. Miron, M. Anastasiei, The geometry of Lagrange spaces: theory and applications, Kluwer Acad. Publ., Dordrecht, 1994 | MR | Zbl

[11] T.N. Pandey, V.K. Chaubey, “The variational problem in Lagrange spaces endowed with $ (\gamma, \beta) $ metric”, Int. J. Pure Appl. Math., 71:4 (2011), 633–638 | MR | Zbl

[12] T.N. Pandey, V.K. Chaubey, “Lagrange spaces with $\beta$-change”, Int. J. Contemp. Math. Sci., 7:45-48 (2012), 2363–2371 | MR | Zbl

[13] S.-S. Chern, Z. Shen, Riemann-Finsler geometry, Nankai Tracts in Mathematics, 6, World Scientific, Hackensack, 2005 | DOI | MR | Zbl

[14] Z. Shen, G. Civi Yildirim, “On a class of projectively flat metrics with constant flag curvature”, Can. J. Math., 60:2 (2008), 443–456 | DOI | MR | Zbl