Milnor-type theorems for left-invariant Riemannian metrics on Lie groups

DOI10.2969/JMSJ/06820669zbMath1353.53058arXiv1501.02485OpenAlexW2963284643WikidataQ115225041 ScholiaQ115225041MaRDI QIDQ296543

Kazuhiro Terada, Hiroshi Tamaru, Takahiro Hashinaga

Publication date: 23 June 2016

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

Full work available at URL: https://arxiv.org/abs/1501.02485

zbMATH Keywords

Lie groupsleft-invariant Riemannian metricsMilnor framesMilnor-type theoremsRicci signaturessolvsolitons

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (9)

Three-dimensional solvsolitons and the minimality of the corresponding submanifolds ⋮ 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 ⋮ Harmonicity of vector fields on the oscillator groups with neutral signature ⋮ A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups ⋮ On the nonexistence of left-invariant Ricci solitons -- a conjecture and examples ⋮ On local isometric embeddings of three-dimensional Lie groups ⋮ Left-invariant symplectic structures on diagonal almost abelian Lie groups

Cites Work

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• The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional lie groups. The unimodular case
• The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
• Einstein solvmanifolds and nilsolitons
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
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