2016/09/09 by Maciej Dunajski, Dunajski, Maciej, Paul Tod +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Myofascial pain diagnosis and treatment #gr-qc #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.1609.02747
arxiv created 2016/09/09 · openalex publication_date 2016/09/09 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.