(α,β)-Metric on Cartan Space

In Finsler geometry, a Cartan space or Cartan manifold refers to a special type of geometrical structure where there is a preferred connection or curvature, often associated with a homogeneous space that carries additional symmetries. In the present research paper, we have deduced necessary and sufficient conditions under which an (α,β)-metric, K(x,ω)=α(x,ω)+ϵβ(x,ω)+2k (β^2 (x,ω))/(α(x,ω))-k^2/3 (β^4 (x,ω))/(α^3 (x,ω)), on a Cartan space admitting h-metrical d-connection becomes a locally Minkowski and conformally flat space.