Nonholonomic frames for Finsler space with infinite series of (α, β) metric

Abstract

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler $ (\alpha, \beta) $-metric. Consequently, we obtained the non-holonomic frame with the help of Riemannian metric $ \alpha^{2}=a_{ij}(x)y^{i}y^{j} $, one form metric $ \beta=b_{i}(x)y^{i} $ and infinite series of $(\alpha, \beta)$ metric such as the forms 

$ I.\;\; (\frac{\beta^{2}}{\beta-\alpha})\alpha =\frac{\alpha \beta^{2}}{\beta-\alpha} $ i.e. product of the infinite series of $ (\alpha, \beta) $-metric and Riemannian metric 

$ II.\;\;(\frac{\beta^{2}}{\beta-\alpha})\beta = \frac{\beta^{3}}{\beta-\alpha}$ i.e. product of the infinite series of $ (\alpha, \beta) $-metric and 1-form metric.