The isometry groups of simply connected 3-dimensional unimodular Lie groups

DOI10.1016/j.geomphys.2011.10.011zbMath1247.22012OpenAlexW1971267223WikidataQ115353243 ScholiaQ115353243MaRDI QIDQ2428143

Ku Yong Ha, Jong Bum Lee

Publication date: 24 April 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2011.10.011

zbMATH Keywords

automorphism groupisometry group3-dimensional Lie groupleft invariant Riemannian metric

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Nilpotent and solvable Lie groups (22E25) General properties and structure of real Lie groups (22E15)

Related Items (11)

The isometry groups of Lorentzian three-dimensional unimodular simply connected Lie groups ⋮ The index of symmetry of three-dimensional Lie groups with a left-invariant metric ⋮ Geometric structures and the Laplace spectrum, Part II ⋮ Isometry groups of three-dimensional Lie groups ⋮ Left invariant degenerate metrics on Lie groups ⋮ Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups ⋮ Control systems on nilpotent Lie groups of dimension \(\leq 4\): equivalence and classification ⋮ Constructions of helicoidal minimal surfaces and minimal annuli in \(\widetilde{E(2)}\) ⋮ The classifying Lie algebroid of a geometric structure. II: \(G\)-structures with connection ⋮ On the Hermitian structures of the sequence of tangent bundles of an affine manifold endowed with a Riemannian metric ⋮ Crystallographic groups of Sol

Cites Work

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• The group of isometries of a left invariant Riemannian metric on a Lie group
• Curvatures of left invariant metrics on Lie groups
• Riemannian isometry groups containing transitive reductive subgroups
• Isometry groups of unimodular simply connected 3-dimensional Lie groups
• The group of isometries of a Riemannian manifold
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• Isometry Groups of Riemannian Solvmanifolds
• Seifert manifolds with fiber spherical space forms
• The Geometries of 3-Manifolds

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