The present article is organized as follows: In the first part, we characterize the important class of special Finsler (α,β)-metric in the form of L=α+α2/β, where α is Riemannian metric and β is differential 1-form to be projectively flat. In the second part, we describe condition for a Finsler space Fn with an (α,β)-metric is of Douglas type. Further we investigate the necessary and sufficient condition for a Finsler space with an (α,β)-metric to be weakly-Berwald space and Berwald space.
International Journal of Pure Mathematical Sciences (Volume 18)
M. Ramesha and S.K. Narasimhamurthy, "Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric", International Journal of Pure Mathematical Sciences, Vol. 18, pp. 1-12, 2017