n =(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)=bi(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).

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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)=bi(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
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[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
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