A Concurrent Generalized Kropina Change

This paper investigates a generalized Kropina metric featuring a specific $\pi$-form. Start with a Finsler manifold $(M,F)$ admits a concurrent $\pi$-vector field $\bar{\phi }$, then, examine the $\phi$-concurrent generalized Kropina change defined by $\widehat{F}=\frac{F^{m+1}}{{\mathrm{\Phi }}^m},{\mathrm{\Phi }}^m>0$, where $\mathrm{\Phi }$ represents the corresponding $1$-form. We investigate the fundamental geometric objects associated with $\widehat{F}$ in an intrinsic manner after adopting this modification and present an example of a Finsler metric that admits a concurrent vector field along with $\widehat{F}$. Also, we prove that the geodesic sprays of $F$ and $\widehat{F}$ can never be projectively related. Moreover, we show $\bar{\phi }$ is not concurrent with respect to $\widehat{F}$. Eventhough, we give a sufficient condition for $\bar{\phi }$ to be concurrent with respect to $\widehat{F}$. Finally, we prove that the $\phi$-concurrent generalized Kropina change ($F⟶\widehat{F}$) preserves the almost rational property of the initial Finsler metric $F$.