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

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 \alpha^{۲}=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^{۴}}{(\beta-\alpha)^{۲}})+\alpha^{۲} =F_{۱}^{۲}+F_{۲}^{۲} i.e. sum of the square of infinite series of (\alpha, \beta) -metric and square of Riemannian metric II.\;\;(\frac{\beta^{۴}}{(\beta-\alpha)^{۲}})+\beta^{۲} =F_{۱}^{۲}+F_{۳}^{۲} i.e. sum of the square of infinite series of (\alpha, \beta) -metric and square of ۱-form metric.

Keywords:

Riemannian metric , One form metric , Infinite series of (\alpha , \beta) -metric , Nonholonomic Finsler frame