On Two-Dimensional Landsberg Space with a Special \((\alpha,\beta)\)-Metric

Authors

  • Gauree Shanker Department of Mathematics and Statistics, Banasthali University, Banasthali, Rajasthan 304022
  • Deepti Choudhary Department of Mathematics and Statistics, Banasthali University, Banasthali, Rajasthan 304022

DOI:

https://doi.org/10.26713/cma.v8i3.329

Keywords:

Berwald space, Cartan connection, Finsler space, Landsberg space, Main scalar

Abstract

The purpose of the present paper is to study a Finsler space with a special \((\alpha,\beta)\)-metric \(L(\alpha,\beta) =\alpha+\beta+\kappa\dfrac{\beta^2}{\alpha}\) \((\epsilon\) and \(k\neq 0\) are real constants) satisfying some conditions. First we find a condition for a Finsler space with a special \((\alpha,\beta)\)-metric to be a Berwald space. Then we show that if a two-dimensional Finsler space with a special \((\alpha,\beta)\)-metric \(L(\alpha,\beta) =\alpha+\beta+\kappa\dfrac{\beta^2}{\alpha}\) \((\epsilon\) and \(k\neq 0\) are real constants) is a Landsberg space, then it is a Berwald space.

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References

P. L. Antonelli: Hand Book of Finsler Geometry, Kluwer Academic Publishers, FTPH 58, (1993).

S. Bacso and M. Matsumoto: Projective changes between Finsler spaces with ((alpha,beta))-metric. Tensor (N.S.) 55(3), (1994), 252-257.

S. Bacso and M. Matsumoto: Reduction theorems of certain Landsberg spaces to Berwald spaces. Publ. Math. Debrecen 48(34), (1996), 357-366.

M. Hashiguchi, S. Hojo and M. Matsumoto: Landsberg spaces of dimension two with ((alpha,beta))-metric. Tensor (N.S.) 57(2), (1996), 145-153.

I. Y. Lee: On two-dimension Landsberg space with a special ((alpha,beta))-metric. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 10(4), (2003), 279-288.

M. Matsumoto: Foundations of Finsler geometry and special Finsler spaces. Kaiseisha Press, Shigaken, otsu, 520, (1986).

C. Shibata, H. Shimada, M. Azuma and H. Yasuda: On Finsler spaces with Randers' metric. Tensor (N.S.) 31(2), (1977), 219-226.

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Published

30-12-2017
CITATION

How to Cite

Shanker, G., & Choudhary, D. (2017). On Two-Dimensional Landsberg Space with a Special \((\alpha,\beta)\)-Metric. Communications in Mathematics and Applications, 8(3), 323–331. https://doi.org/10.26713/cma.v8i3.329

Issue

Vol. 8 No. 3 (2017)

Section

Research Article

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