The holonomy Lie algebras of neutral metrics in dimension four
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Publication:2774897
DOI10.1063/1.1362284zbMath1016.53039OpenAlexW1996395533MaRDI QIDQ2774897
Ryad A. Ghanam, Gerard Thompson
Publication date: 26 February 2002
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.1362284
Structure theory for Lie algebras and superalgebras (17B05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Issues of holonomy in differential geometry (53C29)
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A note on recurrent bivectors in 4-dimensional Lorentz Manifolds ⋮ Walker’s theorem without coordinates ⋮ On four-dimensional paracomplex structures with Norden metrics ⋮ Self-dual Walker metrics with a two-step nilpotent Ricci operator ⋮ The classification of the Weyl conformal tensor in 4-dimensional manifolds of neutral signature ⋮ A study on killing vector fields in four-dimensional spaces ⋮ Almost Kähler-Einstein structures on 8-dimensional Walker manifolds ⋮ De Rham–Wu decomposition of holomorphic Riemannian manifolds ⋮ Holonomy algebras of pseudo-quaternionic-Kählerian manifolds of signature (4,4) ⋮ Holonomy algebras of pseudo-hyper-Kählerian manifolds of index 4 ⋮ Holonomy classification of Lorentz-Kähler manifolds ⋮ Recurrence structures in 4-dimensional manifolds with metric of signature \((+, +, -, -)\) ⋮ The algebra of parallel endomorphisms of a pseudo-Riemannian metric: semi-simple part ⋮ Counterexamples to Goldberg Conjecture with Reversed Orientation on Walker 8-Manifolds of Neutral Signature ⋮ Local rigidity and nonrigidity of symplectic pairs ⋮ Applications of a special generalized quasi-Einstein manifold ⋮ Mathematical properties of a class of four-dimensional neutral signature metrics ⋮ A spinor approach to Walker geometry ⋮ New examples of Einstein metrics in dimension four ⋮ The geometry of 4-dimensional, Ricci-flat manifolds which admit a metric ⋮ Neutral signature Walker-CSI metrics ⋮ Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds ⋮ Spin coefficients for four-dimensional neutral metrics, and null geometry ⋮ Classification of the Weyl curvature spinors of neutral metrics in four dimensions ⋮ Some comparisons of the Weyl conformal tensor and its classification in 4-dimensional Lorentz, neutral or positive definite signatures ⋮ Some properties of para-Kähler–Walker metrics
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