Rank-one Einstein solvmanifolds of dimension 7.
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Publication:1417342
DOI10.1016/S0926-2245(03)00037-8zbMath1045.53032WikidataQ115338008 ScholiaQ115338008MaRDI QIDQ1417342
Publication date: 4 January 2004
Published in: Differential Geometry and its Applications (Search for Journal in Brave)
nilpotent Lie groupssolvmanifoldsleft invariant metricssolvable Lie groupsEinstein homogeneous manifolds
Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Nilpotent and solvable Lie groups (22E25)
Related Items (33)
Three-dimensional solvsolitons and the minimality of the corresponding submanifolds ⋮ Conformally parallel \(G_2\) structures on a class of solvmanifolds ⋮ Purely coclosed \(\mathrm{G}_2\)-structures on 2-step nilpotent Lie groups ⋮ Solutions of the Laplacian flow and coflow of a locally conformal parallel \(\mathrm{G}_2\)-structure ⋮ Classification of 7-dimensional Einstein nilradicals ⋮ Non-compact Einstein manifolds with symmetry ⋮ Explicit Ricci solitons on nilpotent Lie groups ⋮ Coclosed \(\mathrm{G}_{2}\)-structures inducing nilsolitons ⋮ Einstein metrics on bundles over Hyperkähler manifolds ⋮ On the moment map for the variety of Lie algebras. ⋮ Einstein solvmanifolds attached to two-step nilradicals ⋮ Classification of nilsoliton metrics in dimension seven ⋮ Einstein solvmanifolds with a simple Einstein derivation ⋮ Geometric invariants for nilpotent metric Lie algebras with applications to moduli spaces of nilsoliton metrics ⋮ Double extensions on Riemannian Ricci nilsolitons ⋮ Geometry of homogeneous Riemannian manifolds ⋮ Ricci nilsoliton black holes ⋮ The Alekseevskii conjecture in low dimensions ⋮ Einstein solvmanifolds and the pre-Einstein derivation ⋮ Indefinite Einstein metrics on nice Lie groups ⋮ Ricci-flat and Einstein Pseudoriemannian nilmanifolds ⋮ The existence of soliton metrics for nilpotent Lie groups ⋮ Einstein solvmanifolds: Existence and non-existence questions ⋮ Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups ⋮ Moduli of Einstein and non-Einstein nilradicals ⋮ A curve of nilpotent Lie algebras which are not Einstein nilradicals ⋮ The space of solvsolitons in low dimensions ⋮ Solvmanifolds with integrable and non-integrable \(G_{2}\) structures ⋮ Einstein locally conformal calibrated \(G_2\)-structures ⋮ Nice pseudo-Riemannian nilsolitons ⋮ Classification of ordered type soliton metric Lie algebras by a computational approach ⋮ Indefinite nilsolitons and Einstein solvmanifolds ⋮ On the diagonalization of the Ricci flow on Lie groups
Cites Work
- The curvature of homogeneous Siegel domains
- Harmonic analysis on solvable extensions of H-type groups
- Noncompact homogeneous Einstein spaces
- Finding Einstein solvmanifolds by a variational method
- Alekseevskian spaces
- Standard Einstein Solvmanifolds as Critical Points
- CONJUGACY OF POLAR FACTORIZATIONS OF LIE GROUPS
- Complex structures on nilpotent Lie algebras
- Ricci soliton homogeneous nilmanifolds
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