$\mathit{Quasi}$-Einstein metrics play an important role in Finsler geometry, acting as a natural extension of their counterparts in Riemannian geometry \cite{ota}. Recently, Ohta proposed a definition of $N$-Ricci curvature, which brings together the concepts of $S$-curvature and the Ricci curvature in Finsler geometry. In this paper, we introduce the concept of $\mathit{quasi}$-Einstein reversibility for Finsler metrics, which extends the standard $\mathit{quasi}$-Einstein condition in this context. We further investigate $\mathit{quasi}$-Ricci-flat and $\mathit{quasi}$-Einstein Randers metrics in detail. Finally, we demonstrate that every $\mathit{quasi}$-Einstein Randers metric possesses isotropic $S$-curvature, and we establish an equivalence between $\mathit{quasi}$-Einstein reversibility and the $\mathit{quasi}$-Einstein property for Randers metrics.
Mathematical Analysis and Convex Optimization