紧李群上左不变爱因斯坦度量的研究

在本项目中，我们将利用李群李代数理论来研究齐性爱因斯坦度量。主要问题.包括：.（1）紧单李群上左不变非自然可约爱因斯坦度量的研究；.（2）正规齐性爱因斯坦流形上齐性爱因斯坦度量的研究；.（3）紧半单（非单）李群上左不变非自然可约爱因斯坦度量的研究。.本项目的目标是在上述齐性空间上找到新的齐性爱因斯坦度量。

In this project, we will study homogeneous Einstein metrics using the.theory of Lie groups and Lie algebras. Our main problems include:.(1) Study left invariant Einstein metrics on compact simple Lie groups which are not naturally reductive;.(2) Study homogeneous Einstein metrics on normal homogeneous Einstein manifolds;.(3) Study left invariant Einstein metrics on compact semi-simple (non-simple) Lie groups which are not naturally reductive..The aim of this project is to find some new examples of homogeneous Einstein.metrics on those homogeneous spaces.