A family of Einstein Randers metrics

TL;DR

This paper constructs a new family of Einstein Randers metrics with non-constant flag curvature on  using the Hawking Taub-NUT metric and Killing vector fields, expanding the class of known Einstein Finsler geometries.

Contribution

It introduces a 5-parameter family of Einstein Randers metrics with non-constant flag curvature derived from the Hawking Taub-NUT metric and Killing vector fields.

Findings

Constructed a 5-parameter family of Einstein Randers metrics.

Demonstrated these metrics have non-constant flag curvature.

Extended the known examples of Einstein Finsler metrics.

Abstract

Using Hawking Taub-NUT metric $g_a$ on $\mathbf{R}^4$, where $a$ is a positive real number and finding a 4-parameter family of Killing vector fields of $(\mathbf{R}^4,g_a)$, we construct a 5-parameter family of Einstein Randers metrics with non-constant flag curvature.