On the nonexistence of closed timelike geodesics in flat Lorentz 2-step nilmanifolds

DOI10.1090/S0002-9947-02-03114-8zbMath1028.53045MaRDI QIDQ4779894

Mohammed Guediri

Publication date: 28 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Lorentz manifolds2-step nilmanifoldsclosed timelike geodesicsleft-invariant Lorentz metrics2-step nilpotent Lie groups

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (17)

Compact flat spacetimes ⋮ A new class of compact spacetimes without closed causal geodesics ⋮ Complete classification of pseudo \(H\)-type Lie algebras. I ⋮ Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field ⋮ On pseudo-Euclidean Novikov algebras ⋮ On a remarkable class of flat pseudo-Riemannian Lie groups ⋮ On the global hyperbolicity of Lorentz 2-step nilpotent Lie groups ⋮ Lorentzian compact manifolds: isometries and geodesics ⋮ A criterion for global hyperbolicity of left-invariant Lorentz metrics on Lie groups ⋮ On the isometry groups of invariant Lorentzian metrics on the Heisenberg group ⋮ Lorentzian causality theory ⋮ On causality and closed geodesics of compact Lorentzian manifolds and static spacetimes ⋮ Class A spacetimes ⋮ Flat left-invariant pseudo-Riemannian metrics on unimodular Lie groups ⋮ Flat left-invariant pseudo-Riemannian metrics on quadratic Lie groups ⋮ On flat pseudo-Euclidean nilpotent Lie algebras ⋮ Closed timelike geodesics in compact spacetimes

Cites Work

• Three-dimensional affine crystallographic groups
• Flat spacetimes
• Riemannian nilmanifolds attached to Clifford modules
• Left-invariant Lorentz metrics on Lie groups
• Lorentz geometry of 2-step nilpotent Lie groups
• On the existence of closed timelike geodesics in compact spacetimes
• On the Geometry of Groups of Heisenberg Type
• Existence of Closed Timelike Geodesics in Lorentz Spaces
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• Geometry of $2$-step nilpotent groups with a left invariant metric
• The Large Scale Structure of Space-Time
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