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.