A step towards the Alekseevskii conjecture

DOI10.1007/s00208-016-1429-7zbMath1367.53041arXiv1403.5037OpenAlexW2154759141WikidataQ123219707 ScholiaQ123219707MaRDI QIDQ2396221

Michael Jablonski, Peter V Petersen

Publication date: 7 June 2017

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5037

zbMATH Keywords

Einstein metrichomogeneous manifoldAlekseevskii conjecture

Mathematics Subject Classification ID

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

Related Items (14)

Three-dimensional solvsolitons and the minimality of the corresponding submanifolds ⋮ Non-solvable Lie groups with negative Ricci curvature ⋮ On Ricci negative derivations ⋮ On Ricci Negative Lie Groups ⋮ Immortal homogeneous Ricci flows ⋮ Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds ⋮ Non-compact Einstein manifolds with symmetry ⋮ On the signature of the Ricci curvature on nilmanifolds ⋮ The Alekseevskii conjecture in 9 and 10 dimensions ⋮ On the nonexistence of left-invariant Ricci solitons -- a conjecture and examples ⋮ Negative Ricci curvature on some non-solvable Lie groups ⋮ The Alekseevskii conjecture in low dimensions ⋮ Negative Ricci curvature on some non-solvable Lie groups II ⋮ Half-flat structures inducing Einstein metrics on homogeneous spaces

Cites Work

• Unnamed Item
• Homogeneous Ricci solitons are algebraic
• The Alekseevskii conjecture in low dimensions
• Einstein solvmanifolds are standard
• Distinguished orbits of reductive groups
• Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons
• Killing vector fields of constant length on locally symmetric Riemannian manifolds
• Transitive group actions and Ricci curvature properties
• Metrics of negative Ricci curvature on \(\mathrm{SL}(n,\mathbb R)\), \(n\geq 3\)
• Structure of homogeneous Riemann spaces with zero Ricci curvature
• Curvatures of left invariant metrics on Lie groups
• Riemannian isometry groups containing transitive reductive subgroups
• Noncompact homogeneous Einstein spaces
• On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces
• Isometry groups of homogeneous quaternionic Kähler manifolds
• Einstein solvmanifolds have maximal symmetry
• Strongly solvable spaces
• Structure of homogeneous Ricci solitons and the Alekseevskii conjecture
• Homogeneous Einstein spaces of dimension four
• Noncompact homogeneous Einstein 5-manifolds
• Self-adjoint groups
• Ricci soliton solvmanifolds
• A Stratification of the Null Cone Via the Moment Map
• Minimum Vectors for Real Reductive Algebraic Groups
• Homogeneous Manifolds with Negative Curvature. I
• Homogeneous Ricci Solitons in Low Dimensions
• Stratifications with respect to actions of real reductive groups
• Vector fields and Ricci curvature

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