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

Volume 8 Issue 1 January - March 2019

Research Paper

On β -Change Of Special Finsler (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.

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

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).