Theory of Cartan Space with the Generalized Square Metric

The rise of generalized square metrics in Finsler geometry is linked to diverse classifications of (α,β)-metrics, showcasing outstanding geometric properties within this field. In this research paper, we have obtained a necessary and sufficient conditions under which a Cartan space with the generalized square metric, K(x,ω)=([α(x,ω)+β(x,ω)]^(n+1))/([α(x,ω)]^n ), admitting h-metrical d-connection becomes a locally Minkowski and conformally flat space.