Non-compact Einstein manifolds with symmetry

DOI10.1090/jams/1022zbMath1516.53049arXiv2107.04210OpenAlexW3181829129MaRDI QIDQ6039552

Christoph Böhm, Ramiro A. Lafuente

Publication date: 5 May 2023

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.04210

zbMATH Keywords

Einstein manifoldsnegative scalar curvatureLie group actionsAlekseevsky conjecture

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Geometric invariant theory (14L24) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Special Vinberg cones, invariant admissible cubics and special real manifolds, A class of locally inhomogeneous complete quaternionic Kähler manifolds, Einstein metrics on bundles over Hyperkähler manifolds, Einstein hypersurfaces in irreducible symmetric spaces, Homogeneous Einstein metrics and butterflies, Geometry. Abstracts from the workshop held June 12--18, 2022, Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank, Weyl-Einstein structures on conformal solvmanifolds, A classification of left-invariant pseudo-Riemannian metrics on some nilpotent Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classification of nilsoliton metrics in dimension seven
• Negative Ricci curvature on some non-solvable Lie groups
• The Alekseevskii conjecture in low dimensions
• The Riemannian \(L^{2}\) topology on the manifold of Riemannian metrics
• Einstein solvmanifolds are standard
• On the existence of slices for actions of non-compact Lie groups
• Negative Ricci curvature on complex simple Lie groups
• Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons
• Partial differential equations. I: Basic theory
• G-actions and the fundamental group
• The fundamental conjecture for homogeneous Kähler manifolds
• Transitive group actions and Ricci curvature properties
• Metrics of negative Ricci curvature on \(\mathrm{SL}(n,\mathbb R)\), \(n\geq 3\)
• Remarks on the group of isometries of a Riemannian manifold
• Noncompact homogeneous Einstein spaces
• Kähler-Einstein metrics of cohomogeneity one
• Strong rigidity of positive quaternion-Kähler manifolds
• Einstein metrics on \(S^2\)-bundles
• Rank-one Einstein solvmanifolds of dimension 7.
• Selfdual Einstein metrics with torus symmetry
• On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces
• The initial value problem for cohomogeneity one Einstein metrics
• Isometry groups of homogeneous quaternionic Kähler manifolds
• Elliptic partial differential equations of second order
• Immortal homogeneous Ricci flows
• Einstein solvmanifolds have maximal symmetry
• Metrics of negative Ricci curvature
• Finding Einstein solvmanifolds by a variational method
• Alekseevskian spaces
• Polar manifolds and actions
• A Bochner theorem and applications
• The Alekseevskii conjecture in 9 and 10 dimensions
• Geometric structures of collapsing Riemannian manifolds. II
• Non-solvable Lie groups with negative Ricci curvature
• Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
• The collapsing geometry of almost Ricci-flat 4-manifolds
• A class of cubic hypersurfaces and quaternionic Kähler manifolds of co-homogeneity one
• Homogeneous Ricci solitons
• Strongly solvable spaces
• On homogeneous manifolds of negative curvature
• Negative Ricci curvature on some non-solvable Lie groups II
• A family of steady Ricci solitons and Ricci-flat metrics
• Non-Kähler expanding Ricci solitons, Einstein metrics, and exotic cone structures
• A step towards the Alekseevskii conjecture
• Complete intersections with \(S^{1}\)-action
• Construction of Einstein metrics by generalized Dehn filling
• Einstein manifolds
• Dehn filling and Einstein metrics in higher dimensions
• A canonical compatible metric for geometric structures on nilmanifolds
• Structure of homogeneous Ricci solitons and the Alekseevskii conjecture
• Homogeneous Einstein spaces of dimension four
• Noncompact homogeneous Einstein 5-manifolds
• Einstein solvmanifolds and the pre-Einstein derivation
• Ricci soliton solvmanifolds
• Einstein solvmanifolds and nilsolitons
• Riemannian Geometry
• A Stratification of the Null Cone Via the Moment Map
• Isometry Groups of Riemannian Solvmanifolds
• Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes
• Métriques kählériennes et fibrés holomorphes
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Non-compact cohomogeneity one Einstein manifolds
• Complete Ricci Solitons via Estimates on the Soliton Potential
• Einstein extensions of Riemannian manifolds
• Differential Geometry in the Large
• Examples of compact Einstein four-manifolds with negative curvature
• A Perron-type Theorem on the Principal Eigenvalue of Nonsymmetric Elliptic Operators
• Homogeneous Ricci Solitons in Low Dimensions
• Stratifications with respect to actions of real reductive groups
• Families of Linear Operators Depending Upon a Parameter
• Lie groups beyond an introduction
• Ricci soliton homogeneous nilmanifolds