Einstein metrics on compact Lie groups which are not naturally reductive

TL;DR

This paper proves the existence of non-naturally reductive Einstein metrics on various compact simple Lie groups, expanding the class of known Einstein metrics beyond naturally reductive cases.

Contribution

It establishes the existence of non-naturally reductive Einstein metrics on SO(n), Sp(n), E6, E7, and E8, for the first time on these groups.

Findings

Existence of non-naturally reductive Einstein metrics on SO(n) for n ≥ 11.

Existence of such metrics on Sp(n) for n ≥ 3.

Existence of such metrics on E6, E7, and E8.

Abstract

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by J. E. D'Atri and W. Ziller in 1979. In 1996 the second author obtained non-naturally reductive Einstein metrics on the Lie group SU(n) for $n \ge 6$, by using a method of Riemannian submersions. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) ($n \geq 11$), $Sp(n)$ ($n \geq 3$), $E_6$, $E_7$, and $E_8$.