Doubly extended Lie groups -- curvature, holonomy and parallel spinors.

DOI10.1016/S0926-2245(03)00034-2zbMath1066.53115arXivmath/0203189OpenAlexW1980601969WikidataQ115338017 ScholiaQ115338017MaRDI QIDQ1417338

Helga Baum, Ines Kath

Publication date: 4 January 2004

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203189

zbMATH Keywords

metricsBiinvariantDoubly extended Lie groupsHolonomyNon-semisimple symmetric spacesParallel spinors

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Spin and Spin({}^c) geometry (53C27) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Issues of holonomy in differential geometry (53C29) General properties and structure of real Lie groups (22E15)

Related Items

Naturally reductive pseudo-Riemannian spaces ⋮ Complete description of invariant, associative pseudo-Euclidean metrics on left Leibniz algebras via quadratic Lie algebras ⋮ Conformal properties of indefinite bi-invariant metrics ⋮ Lie bialgebras of complex type and associated Poisson Lie groups ⋮ On the isometry groups of invariant Lorentzian metrics on the Heisenberg group ⋮ Lorentzian Lie n-algebras

Cites Work

• Complete Riemannian manifolds with imaginary Killing spinors
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Symmetric, invariant, non-degenerate bilinear form on a Lie algebra
• Parallel spinors and parallel forms
• Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds
• On the holonomy of pseudo-Riemannian manifolds of signature \((2,2+n)\)
• Twistor spinors on Lorentzian symmetric spaces
• A note on real Killing spinors in Weyl geometry
• Killing spinors on Lorentzian manifolds
• On non-simply connected manifolds with non-trivial parallel spinors
• Real Killing spinors and holonomy
• Parallel spinors and holonomy groups
• Algèbres de Lie et produit scalaire invariant
• Pseudo-Riemannian symmetric spaces
• On the supersymmetries of anti-de Sitter vacua
• Lorentzian symmetric spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item