Self-duality of metrics of type \((2,2)\) on four-dimensional manifolds

DOI10.2748/tmj/1178225150zbMath0880.53052OpenAlexW2164368452MaRDI QIDQ1365343

Hiroyuki Kamada, Yoshinori Machida

Publication date: 8 February 1998

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225150

zbMATH Keywords

curvature tensorself-dualityWeyl conformal tensorpseudo-Riemannian 4-manifolds(2,2)-metrics

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (7)

Almost Kähler-Einstein structures on 8-dimensional Walker manifolds ⋮ Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures ⋮ Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues ⋮ Twistor theory of manifolds with Grassmannian structures ⋮ Classification of the Weyl curvature spinors of neutral metrics in four dimensions ⋮ Compact scalar-flat indefinite Kähler surfaces with Hamiltonian \(S^{1}\)-symmetry ⋮ Four-dimensional indefinite Kähler Osserman manifolds

Cites Work

• Fields of 2-planes and two kinds of almost complex structures on compact 4-dimensional manifolds
• Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten. (Plane element fields in 4-dimensional manifolds)
• Counter-examples to the generalized positive action conjecture
• Self-dual solutions to Euclidean gravity
• Self-dual manifolds with positive Ricci curvature
• Explicit self-dual metrics on \({\mathbb{C}}{\mathbb{P}}_ 2\#\cdots \#{\mathbb{C}}{\mathbb{P}}_ 2\)
• Self-duality in four-dimensional Riemannian geometry
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