Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20240505On Zermelo’s navigation problem and weighted Einstein Randers metrics540310.22060/ajmc.2024.22745.1189ENIllatraKhamonezhadDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, IranBahmanRezaeiDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, IranMehranGabraniDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran0000-0002-4489-0477Journal Article20231010This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, $F$ and $\tilde{F}$ are considered, which are generated by navigation representations $(h, W)$ and $(F, V)$, respectively, where $W$ represents a vector field, and $V$ represents a conformal vector field on the manifold $M$. The main focus is on identifying the necessary and sufficient condition for the Randers metric $F$ to qualify as a quasi-Einstein metric. Additionally; we establish the relationship between the curvatures of the given Finsler metrics $F$ and $\tilde{F}$.