2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163154We 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.latex 2e, 15 pages, no figureGeneral Relativity and Quantum Cosmologytext