Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON A FINSLER SPACE WITH (α, β)-METRIC AND CERTAIN METRICAL NON-LINEAR CONNECTION

  • Published : 2006.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

Keywords

References

  1. P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, Kluwer Acad. Publ., The Netherlands, 1993
  2. M. Hashiguchi, On conformal transformations of Finsler metrics, J. Math. Kyoto Univ. 16 (1976), 25-50 https://doi.org/10.1215/kjm/1250522956
  3. Y. Ichijyo, On the condition for a {V, H}-manifold to be locally Mincowskian or coformally flat, J. Math. Tokushima Univ. 12 (1979), 13-21
  4. Y. Ichijyo and M. Hashiguchi, On the condition that a Randers space be conformal flat, Rep. Fac. Sci. Kagoshima Univ., (Math. Phys. Chem.) 22 (1989), 7-14
  5. L. Kozma and S. Baran, On metrical homogeneous connections of a Finsler point space, Publ. Math. Debrecen 49 (1996), 59-68
  6. M. Matsumoto, Theory of Finsler spaces with (${\alpha},{\beta}$)-metric, Rep. on Math. Phys.31 (1992), 43-83 https://doi.org/10.1016/0034-4877(92)90005-L

Cited by

  1. Randers space with special nonlinear connection vol.29, pp.1, 2008, https://doi.org/10.1134/S1995080208010071
  2. On an R-Randersmth-Root Space vol.2013, 2013, https://doi.org/10.1155/2013/649168