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On β -Change Of Specialfinsler (α, β)-Metrics Of Dougls Type

M. Ramesha*, S. K. Narasimhamurthy**

*Department of Mathematics, School of Engineering and Technology, Jain Global Campus, Jakkasandra, Bangalore, Karnataka, India.

** Department of P.G. Studies and Research in Mathematics, Kuvempu University.

Periodicity:January - March'2019
DOI : https://doi.org/10.26634/jmat.8.1.16186

Abstract

Let Fⁿ =(M, L) be an n-dimensional Finsler manifold, and Let L and L be the two Finsler metrics. For a differential one form β(x,dx)=b_i(x)dxⁱ on M, G. Randers, in 1941, introduced a special Finsler space defined by the change L =L+β, where L is i Riemannian, to consider a unified field theory. For a β-change of Finsler metric, the differential one-form β plays a very important role. With the above observations, in this article, the authors have tried to study the necessary and sufficient n condition for Finsler space Fⁿ which is transformed by a b-change of Finsler space Fⁿ with (α, β)-metric to be of Douglas type. And also we are discussing the different classes of (α, β)-metrics of Finsler spaces Fⁿ are discussed, which is obtained by a β-change of a Finsler space Fⁿ is of Douglas type. The terminology and notations are referred to the Matsumoto's monograph (Matsumoto, 1992).

Keywords

Finsler space, (α, β )-metrics, Randers change, Douglas space

How to Cite this Article?

Ramesha, M., & Narasimhamurthy, S. K . (2019). On beta-Change of Special Finsler (alpha,beta)-Metrics of Dougls Type. i-manager's Journal on Mathematics, 8(1), 24-34 https://doi.org/10.26634/jmat.8.1.16186

References

[1]. Antonelli, P. L., Ingarden, R. S., & Matsumoto, M. (1993). The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology Kluwer.

[2]. Aveesh, S. T., & Narasimhamurthy, S. K. (2013). Douglas Space With A r^th Series (α, β)-metric. JMI International Journal of Mathematical Science, 4(1), 1-9.

[3]. Bácsó, S. (1997). On Finsler spaces of Douglas type. A generalization of the notion of Berwald space. Publ. Math. Debrecen, 51, 385-406.

[4]. Li, B., Shen, Y., & Shen, Z. (2009). On a class of Douglas metrics. Studia Scientiarum Mathematicarum Hungarica, 46(3), 355-365.

[5]. Matsumoto, M. (1974). On Finsler spaces with Randers' metric and special forms of important tensors. Journal of mathematics of Kyoto University, 14(3), 477-498.

[6]. Matsumoto, M. (1986). Foundations of Finsler Geometry and Special Finsler Spaces. Kaiseisha Press.

[7]. Matsumoto, M. (1992). Theory of Finsler spaces with (α,β)-metric. Reports on Mathematical Physics, 31(1), 43-83.

[8]. Matsumoto, M. (1998a). Finsler Spaces With (α, β)-Metric of Douglas Type. Tensori: New Series, 60(2), 123-134.

[9]. Matsumoto, M. (1998b). Projective Randers change of P-reducible Finsler spaces. Tensor. New series, 59, 6-11.

[10]. Park, H. S., & Choi, E. S. (1999). Finsler spaces with an approximate Matsumoto metric of Douglas type. Comm. Korean. Math. Soc.,14(3), 535-544.

[11]. Park, H. S., & Lee, I. Y. (2001a). The Randers changes of Finsler spaces with (α, β)-metrics of Douglas type. J. Korean Math. Soc., 38(3), 503-521.

[12]. Park, H. S., & Lee, Y. D. (2001b). Finsler Spaces With Certain(α, β)-Metric of Douglas Type. Communications of the Korean Mathematical Society, 16(4), 649-658.

[13]. Ramesha, M., & Narasimhamurthy, S. K. (2017). Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric. International Journal of Pure Mathematical Sciences, 18, 1-12, https://doi.org/10.18052/www.scipress.com/ IJPMS.18.1

[14]. Randers, G. (1941). On an asymmetrical metric in the four-space of general relativity. Physical Review, 59(2),195-199.

[15]. Shibata, C., Shimada, H., Azuma, M., & Yasda, H. (1977). On Finsler space with Randers metric, Tensors: N.S., 31, 219- 226.

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