Four-dimensional manifolds with degenerate self-dual Weyl curvature operator

DOI10.1007/s10455-007-9101-9zbMath1181.53030OpenAlexW1972423296MaRDI QIDQ944913

Eduardo García-Río, Alexandre Cortés-Ayaso, José Carlos Díaz-Ramos

Publication date: 10 September 2008

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-007-9101-9

zbMATH Keywords

Walker metricPara-Hermitian and para-Kähler structureSelf-dual Weyl curvature tensor

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items

Geometric structures over four-dimensional generalized symmetric spaces, GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS, Geometric realizations of curvature models by manifolds with constant scalar curvature

Cites Work

• Isotropic Kähler hyperbolic twistor spaces
• Fields of 2-planes and two kinds of almost complex structures on compact 4-dimensional manifolds
• Indefinite Einstein hypersurfaces with nilpotent shape operators
• Almost Kähler Walker 4-manifolds
• Curvature characterization and classification of rank-one symmetric spaces
• Hermitian and Kählerian geometry in relativity
• Pseudo-Chern classes and opposite Chern classes of indefinite almost Hermitian manifolds
• Generalized Goldberg-Sachs theorems for pseudo-Riemannian four-manifolds
• Anti-Kählerian manifolds
• A survey on paracomplex geometry
• Curvature vs. almost Hermitian structures
• Isotropic Kähler structures on Engel 4-manifolds
• Complete \(k\)-curvature homogeneous pseudo-Riemannian manifolds
• Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators
• Para-Hermitian and paraquaternionic manifolds
• Bochner-Kähler metrics
• Walker’s theorem without coordinates
• Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues
• Null geodesic surfaces and Goldberg–Sachs theorem in complex Riemannian spaces
• Sur l'holonomie des variétés pseudo-riemanniennes de signature $(n,n)$
• The Riemannian Goldberg–Sachs Theorem
• CANONICAL FORM FOR A RIEMANNIAN SPACE WITH A PARALLEL FIELD OF NULL PLANES
• Hitchin-Thorpe-type inequalities for pseudo-Riemannian 4-manifolds of metric signature \((++--)\)