Riemannian geometry on contact Lie groups

DOI10.1007/s10711-008-9236-2zbMath1138.53061arXiv1402.5038OpenAlexW3101630980MaRDI QIDQ2427428

André Diatta

Publication date: 13 May 2008

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5038

zbMATH Keywords

Lie groupsEinstein solvmanifoldinvariant contact structureinvariant Riemann structure

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global theory of symplectic and contact manifolds (53D35) Contact manifolds (general theory) (53D10)

Related Items

Non existence of homogeneous contact metric manifolds of non positive curvature ⋮ Characterization of contact Lie superalgebras ⋮ Left invariant contact structures on Lie groups ⋮ A class of Sasakian 5-manifolds ⋮ Complex, symplectic, and contact structures on low-dimensional Lie groups

Cites Work

• On contact manifolds
• Some global properties of contact structures
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• The fundamental conjecture for homogeneous Kähler manifolds
• On Lie groups with left-invariant symplectic or Kählerian structures
• Kähler Lie algebras and double extension
• Contact manifolds in Riemannian geometry
• Curvatures of left invariant metrics on Lie groups
• On the non-existence of flat contact metric structures
• Left-invariant Lorentz metrics on Lie groups
• Noncompact homogeneous Einstein spaces
• Generalized Lie bialgebras and Jacobi structures on Lie groups.
• Classical Yang-Baxter equation and left invariant affine geometry on Lie groups
• Symplectic double extension of a symplectic Lie group
• Algèbres de Lie et produit scalaire invariant
• Algebres de lie orthogonales modules orthogonaux
• Symplectic Homogeneous Spaces