Invariant metrics on Lie groups

DOI10.3934/JGM.2015.7.517zbMath1404.53032OpenAlexW2526748719MaRDI QIDQ888766

Gerard Thompson

Publication date: 2 November 2015

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2015.7.517

zbMATH Keywords

Lie algebraLie groupKilling vector fieldinvariant Riemannian metric

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Lie algebras of Lie groups (22E60) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Connections (general theory) (53C05) Methods of local Riemannian geometry (53B21)

Related Items (1)

Six-dimensional Lie-Einstein metrics

Cites Work

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• A left-symmetric algebraic approach to left invariant flat (pseudo-)metrics on Lie groups
• Killing's equations for invariant metrics on Lie groups
• The space of left-invariant metrics on a Lie group up to isometry and scaling
• Curvatures of left invariant metrics on Lie groups
• Cyclic metric Lie groups
• Novikov algebras carrying an invariant Lorentzian symmetric bilinear form
• Left-Invariant Pseudo-Einstein Metrics on Lie Groups
• Left Invariant Einstein–Randers Metrics on Compact Lie Groups
• Invariants of real low dimension Lie algebras
• Classification of 4-dimensional homogeneous weakly einstein manifolds

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