New non-naturally reductive Einstein metrics on exceptional simple Lie groups

作者：Chen, Huibin; Chen, Zhiqi; Deng, Shaoqiang^*

来源：Journal of Geometry and Physics, 2018, 124: 268-285.

DOI：10.1016/j.geomphys.2017.09.011

• Einstein metric
• Ricci curvature
• Exceptional simple Lie group

In this article, we construct several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are found through the decomposition arising from generalized Wallach spaces. Using the decomposition corresponding to the two involutions, we calculate the non-zero coefficients in the formulas of the components of Ricci tensor with respect to the given metrics. The Einstein metrics are obtained as solutions of a system of polynomial equations, which we manipulate by symbolic computations using Grobner bases. In particular, we discuss the concrete numbers of non-naturally reductive Einstein metrics for each case up to isometry and homothety.

• 出版日期2018-1
• 单位南开大学