Intrinsic Properties of Finsler Space with a cubic change in the Matsumoto Metric

In this paper, we investigate Finsler space with a cubic modification of the Matsumoto metric, given by F=γ²γ-β, where γ is a cubic metric and β is one form metric. We identify the fundamental characteristics of this modified metric. The reducibility of the Cartan torsion tensor is a key factor, as it measures how closely a Finsler metric approximates a Riemannian metric. Specifically, if Cᵢⱼₖ vanishes, the Finsler metric becomes Riemannian. Accordingly, we analyze various forms of the Cartan torsion tensor's reducibility within the context of this cubic-changed Matsumoto metric. We also establish conditions for determining whether the Finsler space is quasi C-reducible, semi C-reducible, C-reducible and C2-like.