The space of left-invariant metrics on a Lie group up to isometry and scaling

DOI10.1007/s00229-010-0419-4zbMath1230.53048OpenAlexW2089521284WikidataQ115388361 ScholiaQ115388361MaRDI QIDQ533688

Hiroshi Kodama, Atsushi Takahara, Hiroshi Tamaru

Publication date: 4 May 2011

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0419-4

zbMATH Keywords

Lie groupisometric actionsorbit spaces

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30)

Related Items (19)

Three-dimensional solvsolitons and the minimality of the corresponding submanifolds ⋮ The index of symmetry of three-dimensional Lie groups with a left-invariant metric ⋮ Milnor-type theorems for left-invariant Riemannian metrics on Lie groups ⋮ Isometry groups of three-dimensional Lie groups ⋮ Unnamed Item ⋮ Invariant metrics on Lie groups ⋮ Geometry of cotangent bundle of Heisenberg group ⋮ Classification of left invariant Riemannian metrics on complex hyperbolic space ⋮ A classification of left-invariant symplectic structures on some Lie groups ⋮ Examples of hyperpolar actions of the automorphism groups of Lie algebras ⋮ A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups ⋮ The Solvable Models of Noncompact Real Two-Plane Grassmannians and Some Applications ⋮ On the nonexistence of left-invariant Ricci solitons -- a conjecture and examples ⋮ Metrics on 4-dimensional unimodular Lie groups ⋮ Six-dimensional Lie-Einstein metrics ⋮ The Space of Left-Invariant Riemannian Metrics ⋮ On local isometric embeddings of three-dimensional Lie groups ⋮ A classification of left-invariant pseudo-Riemannian metrics on some nilpotent Lie groups ⋮ Left-invariant symplectic structures on diagonal almost abelian Lie groups

Cites Work

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• Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
• Isometry groups on homogeneous nilmanifolds
• Critical point theory and submanifold geometry
• Curvatures of left invariant metrics on Lie groups
• Degenerations of Lie algebras and geometry of Lie groups
• Homogeneous codimension one foliations on noncompact symmetric spaces.
• Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
• Einstein solvmanifolds and nilsolitons
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• Lie groups beyond an introduction

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