Bach-flat Lie groups in dimension 4

DOI10.1016/j.crma.2013.04.011zbMath1269.53052arXiv1303.4527OpenAlexW2031952711WikidataQ115358220 ScholiaQ115358220MaRDI QIDQ351388

Elsa Abbena, Sergio Garbiero, S. M. Salamon

Publication date: 11 July 2013

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4527

zbMATH Keywords

solvable Lie groupsleft-invariant Riemannian metricsBach tensor

Mathematics Subject Classification ID

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

Related Items (9)

Four-Dimensional Homogeneous Generalizations of Einstein Metrics ⋮ Bach-flat isotropic gradient Ricci solitons ⋮ Conformally Einstein Lorentzian Lie groups: extensions of the Euclidean and Poincaré groups ⋮ Constructing Bach flat manifolds of signature (2, 2) using the modified Riemannian extension ⋮ Constant scalar curvature metrics on Hirzebruch surfaces ⋮ Gradient ambient obstruction solitons on homogeneous manifolds ⋮ Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds ⋮ Bach flow ⋮ Homogeneous conformal \(C\)-spaces in dimension four

Cites Work

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• Ambitoric geometry. I: Einstein metrics and extremal ambikähler structures
• Conformal Einstein spaces
• Curvatures of left invariant metrics on Lie groups
• Bach-flat asymptotically locally Euclidean metrics
• Homogeneous Einstein spaces of dimension four
• Bach-flat gradient steady Ricci solitons
• Non-vacuum twisting type-N metrics
• Invariant strong KT geometry on four-dimensional solvable Lie groups
• Hypercomplex structures on four-dimensional Lie groups
• Conformal Einstein spaces in \(n\)-dimensions

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