Bianchi III and V Einstein metrics

TL;DR

This paper derives diagonal Einstein metrics for Bianchi III and V models in both Minkowski and Euclidean signatures, revealing integrable geodesic flows in Bianchi III cases.

Contribution

It provides explicit Einstein metrics for Bianchi III and V, including their signatures, and demonstrates integrability of geodesic flow for Bianchi III.

Findings

Explicit Einstein metrics for Bianchi III and V.

Integrability of geodesic flow in Bianchi III metrics.

Metrics applicable to both Minkowski and Euclidean signatures.

Abstract

We present diagonal Einstein metrics for Bianchi III and V, both for minkowskian and euclidean signatures and we show that the Einstein Bianchi III metrics have an integrable geodesic flow.