intrinsic properties of finsler space with a cubic change in infinite series metric

In this paper, we investigate a finsler space characterized by a cubic changed infinite series metric given by f(γ, β)=β2/(β-γ_. we derive the fundamental tensors necessary to describe the geometric properties of this finsler space. additionally, we determine the conditions under which this finsler space with the cubic modified infinite series metric can be simplified into special types of finsler spaces, including quasi-c-reducible, semi-c-reducible, c-reducible, and c2-like finsler spaces, based on its various forms of the cartan tensor.