Cheng, XinyueShen, Zhongmin2017-06-072017-06-072017-01Cheng, X., & Shen, Z. (2017). Einstein Finsler metrics and killing vector fields on Riemannian manifolds. Science China Mathematics, 60(1), 83-98. doi:10.1007/s11425-016-0303-6https://hdl.handle.net/1805/12892We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S3 with Ric = 2F2, Ric = 0 and Ric = -2F2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.enPublisher PolicyKilling vector fieldFinsler metric(a, ß)-metricArticle