on zermelo’s navigation problem and weighted einstein randers metrics

This paper investigates a specific form of weighted ricci curvature known as the quasi-einstein metric. two finsler metrics, f and 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 f˜.