A non Ricci-flat Einstein pseudo-Riemannian metric on a 7-dimensional nilmanifold

DOI10.36045/j.bbms.210210OpenAlexW3045271595WikidataQ115220336 ScholiaQ115220336MaRDI QIDQ2139112

Marco Freibert, Jonatan Sánchez, Marisa Fernández

Publication date: 17 May 2022

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.13398

zbMATH Keywords

Ricci curvaturenilpotent Lie groupsEinstein pseudo-Riemannian metrics\(G_2^\ast\)-structures

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Nilpotent and solvable Lie groups (22E25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items

Ricci-flat and Einstein Pseudoriemannian nilmanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Four-dimensional Lorentzian Lie groups
• Laplacian flow for closed \(\mathrm{G}_{2}\) structures: Shi-type estimates, uniqueness and compactness
• Einstein solvmanifolds: Existence and non-existence questions
• Nilmanifolds with a calibrated \(G_{2}\)-structure
• Riemannian manifolds with structure group \(G_ 2\)
• On the geometry of closed \(G_{2}\)-structures
• On the nilpotent Lie algebras of dimension \(\leq 7)\)
• Metrics with exceptional holonomy
• Curvatures of left invariant metrics on Lie groups
• \(G^*_{2(2)}\)-structures on pseudo-Riemannian manifolds
• The geometry of three-forms in six dimensions.
• Einstein nilpotent Lie groups
• Indefinite Einstein metrics on nice Lie groups
• Ricci-flat and Einstein Pseudoriemannian nilmanifolds
• \(G_2\)-structures on Einstein solvmanifolds
• Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension
• Einstein warped \(\mathrm{G}_{2}\) and spin(7) manifolds
• Torsion-free \(G^*_{2(2)}\)-structures with full holonomy on nilmanifolds
• Laplacian flow of closed \(G_2\)-structures inducing nilsolitons
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups
• FLOWS OF G2-STRUCTURES, I
• Holonomy groups of ${{G}_{2}^*}$-manifolds
• Complex structures on nilpotent Lie algebras