%0 Journal Article
%T On Zermelo’s navigation problem and weighted Einstein Randers metrics
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Khamonezhad, Illatra
%A Rezaei, Bahman
%A Gabrani, Mehran
%D 2024
%\ 05/05/2024
%V
%N
%P -
%! On Zermelo’s navigation problem and weighted Einstein Randers metrics
%K weighted Ricci curvature
%K navigation problem
%K conformal vector field
%R 10.22060/ajmc.2024.22745.1189
%X This 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 $\tilde{F}$.
%U