A Concurrent Generalized Kropina Change

This paper investigates a generalized Kropina metric featuring a specific π-form. Start with a Finsler manifold $(M,F)$ admits a concurrent π-vector field φ̄, then, examine the φ-concurrent generalized Kropina change defined by F=Fᵐ⁺¹Φᵐ, where Φ represents the corresponding $1$-form, Φᵐ>0. We investigate the fundamental geometric objects associated with F in an intrinsic manner after adopting this modification and present an example of a Finsler metric that admits a concurrent vector field along with F. Also, we prove that the geodesic sprays of F and F can never be projectively related. Moreover, we show φ̄ is not concurrent with respect to F. Eventhough, we give a sufficient condition for φ̄ to be concurrent with respect to F. Finally, we use a coordinate-study in proving that the φ-concurrent generalized Kropina change (F F) preserves the almost rational property of the initial Finsler metric F.