Sur l'holonomie des variétés pseudo-riemanniennes de signature $(n,n)$

DOI10.24033/bsmf.2300zbMath0916.53033OpenAlexW2514791618MaRDI QIDQ4346069

Lionel Bérard Bergery, Aziz Ikemakhen

Publication date: 7 October 1997

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1997__125_1_93_0

zbMATH Keywords

holonomy groupspseudo-Riemannian manifolds

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Connections (general theory) (53C05)

Related Items (21)

Holonomy Groups and Algebras ⋮ Nearly para-Kähler geometry on Lie groups ⋮ Almost Kähler Walker 4-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 ⋮ The algebra of parallel endomorphisms of a pseudo-Riemannian metric: semi-simple part ⋮ Geometry and holonomy of indecomposable cones ⋮ Conical Ricci-flat nearly para-Kähler manifolds ⋮ Parallel pure spinors and holonomy ⋮ Four-dimensional manifolds with degenerate self-dual Weyl curvature operator ⋮ A spinor approach to Walker geometry ⋮ The geometry of modified Riemannian extensions ⋮ Representations admitting two pairs of supplementary invariant spaces ⋮ Supersymmetric Killing structures ⋮ Classification of the Weyl curvature spinors of neutral metrics in four dimensions ⋮ On holonomy of Weyl connections in Lorentzian signature ⋮ Para-Kähler-Einstein \(4\)-manifolds and non-integrable twistor distributions ⋮ Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds ⋮ The uniqueness in the de Rham-Wu decomposition ⋮ Null Kähler geometry and isomonodromic deformations

Cites Work

• On the transitivity of holonomy systems
• Metrics with exceptional holonomy
• On the holonomy of pseudo-Riemannian manifolds of signature \((2,2+n)\)
• On the construction of some complete metrics with exceptional holonomy
• Holonomy groups of indefinite metrics
• On the de Rham decomposition theorem
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• Les espaces symétriques noncompacts
• Métriques kählériennes et fibrés holomorphes
• Pseudo-Riemannian symmetric spaces
• Calabi's conjecture and some new results in algebraic geometry
• Lorentzian symmetric spaces
• A Theorem on Holonomy
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