Non-Riemannian Einstein-Randers metrics on $E_6/A_4$ and $E_6/A_1$

TL;DR

This paper demonstrates the existence of Non-Riemannian Einstein-Randers metrics on specific homogeneous spaces derived from the exceptional Lie group E6, expanding understanding of Einstein metrics beyond Riemannian geometry.

Contribution

It proves that the homogeneous spaces E6/A4 and E6/A1 admit Non-Riemannian Einstein-Randers metrics, a novel extension in the study of Einstein metrics on these spaces.

Findings

Existence of Einstein metrics on E6/A4 and E6/A1

Existence of Non-Riemannian Einstein-Randers metrics on these spaces

Invariant properties under specific group actions

Abstract

In this paper, we first prove that homogeneous spaces $E_6/A_4$ and $E_6/A_1$ admit Einstein metrics which are $Ad(T\times A_1\times A_4)$-invariant, and then show that they admit Non-Riemannian Einstein-Randers metrics.