2000/03/25 by Vestislav Apostolov, Paul Gauduchon, Apostolov, Vestislav +1 · 1 citation
Mathematics · Physics and Astronomy · #53B35 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dual (grammatical number) #Einstein #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hermitian matrix #Mathematical physics #Mathematics #Mathematics Subject Classification #Philosophy #Physics #Pure mathematics #Quotient #Ricci-flat manifold #Scalar curvature #math.DG #msc:53B35 #msc:53C55
paper · pdf · doi:10.48550/arxiv.math/0003162
More typos corrected, 39 pages
openalex publication_date 2000/03/25 · arxiv created 2000/08/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide a local classification of self-dual Einstein Riemannian four manifolds admitting a positively oriented Hermitian structure and characterize those which carry a hyperhermitian, non-hyperkählerian structure compatible with the negative orientation. We finally show that self-dual Einstein 4-manifolds obtained as quaternionic quotients of the Wolf spaces \mathbb HP2, \mathbb HH2, SU(4)/S(U(2)U(2)), and SU(2,2)/S(U(2)U(2)) are always Hermitian.