rigidity of weak einstein-randers spaces

The randers metrics are popular metrics similar to the riemannian metrics, frequently used in physical and geometric studies. the weak einstein-finsler metrics are a natural gener-alization of the einstein-finsler metrics. our proof shows that if (m, f ) is a simply-connected and compact randers manifold and f is a weak einstein-douglas metric, then every special projective vec-tor field is killing on (m, f ). furthermore, we demonstrate that if a connected and compact manifold m of dimension n ≥ 3 ad-mits a weak einstein-randers metric with zermelo navigation data (h, w ), then either the s-curvature of (m, f ) vanishes, or (m, h)is isometric to a euclidean sphere sn(√k), with a radius of 1/√k, for some positive integer k.