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 generalization 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 vector field is Killing on (M,F). Furthermore, we demonstrate that if a connected and compact manifold M of dimension n \geq ۳ admits 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 {\mathbb{S}^n}(\sqrt{k}), with a radius of ۱/\sqrt{k}, for some positive integer k.

کلیدواژه ها:

Projective vector fields ، Conformal vector fields ، Randers metric ، Weak Einstein ، S-curvature ، rigidity