本项目计划用李群、李代数理论作为工具，研究齐性Einstein-Finsler流形。在一般情形，我们希望得到若干齐性流形上存在不变Einstein度量的充分条件，进而构造新的有重要意义的实例。在Randers情形，我们期望得到齐性流形上存在Einstein流形的充分必要条件，并在某些特殊流形上给出不变Einstein-Randers度量的完全分类。

In this project, we propose to study homogeneous Einstein-Finsler manifolds by applying the theory of Lie groups and Lie algebras. In the general case, we hope to obtain some sufficient conditions for the existence of invariant Einstein-Finsler metrics, and construct new significant examples based on the conditions. In the special case of Randers metrics, we hope to obtain the necessary and sufficient condition for the existence of invariant Einstein-Randers metrics on homogeneous manifolds, and give a complete classification of such metrics on some special homogeneous manifolds.