The signature of the Ricci curvature of left-invariant Riemannian metrics on nilpotent Lie groups

DOI10.1016/j.difgeo.2016.03.004zbMath1339.53051arXiv1507.02239OpenAlexW2962717258WikidataQ115355710 ScholiaQ115355710MaRDI QIDQ288864

F. Blanchet-Sadri, M. Dambrine

Publication date: 27 May 2016

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02239

zbMATH Keywords

nilpotent Lie algebrasleft invariant metricssignature Ricci curvature

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Nilpotent and solvable Lie groups (22E25) Global Riemannian geometry, including pinching (53C20) Solvable, nilpotent (super)algebras (17B30)

Related Items (2)

New supersymmetric vacua on solvmanifolds ⋮ On the signature of the Ricci curvature on nilmanifolds

Cites Work

• Einstein solvmanifolds: Existence and non-existence questions
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• Einstein solvmanifolds with a simple Einstein derivation
• Curvatures of left invariant metrics on Lie groups
• Negative eigenvalues of the Ricci operator of solvable metric Lie algebras
• Ricci curvatures of left-invariant Riemannian metrics on five-dimensional nilpotent Lie groups
• The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case

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