On gradient Ricci solitons with symmetry

DOI10.1090/S0002-9939-09-09723-8zbMath1168.53021arXiv0710.3595OpenAlexW2072093844MaRDI QIDQ3629432

Publication date: 27 May 2009

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

Full work available at URL: https://arxiv.org/abs/0710.3595

zbMATH Keywords

rigidity Killing field gradient Ricci soliton maximal symmetry

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Non-trivial \(m\)-quasi-Einstein metrics on quadratic Lie groups ⋮ Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ Four-Dimensional Homogeneous Generalizations of Einstein Metrics ⋮ On gradient Ricci solitons with constant scalar curvature ⋮ Laplacian flow of closed \(G_2\)-structures inducing nilsolitons ⋮ On some rotationally symmetric gradient pseudo-Kähler-Ricci solitons ⋮ Immortal homogeneous Ricci flows ⋮ Left invariant pseudo-Riemannian metrics on solvable Lie groups ⋮ Quasi-Einstein manifolds endowed with a parallel vector field ⋮ SOME GAP THEOREMS FOR GRADIENT RICCI SOLITONS ⋮ On generalized \(m\)-quasi-Einstein manifolds with constant Ricci curvatures ⋮ Rigidity of gradient Einstein shrinkers ⋮ The Ricci soliton equation and the structure of homogeneous Gödel-type spacetimes ⋮ Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds ⋮ Rigidity of homogeneous gradient soliton metrics and related equations ⋮ Locally conformally flat Lorentzian gradient Ricci solitons ⋮ Some results on conformal geometry of gradient Ricci solitons ⋮ Some results on \(h\)-almost Ricci-Bourguignon soliton ⋮ On the classification of gradient Ricci solitons ⋮ Four-dimensional homogeneous Kähler Ricci solitons ⋮ Some uniqueness results for Ricci solitons ⋮ Gradient Ricci solitons on multiply warped product manifolds ⋮ Homogeneous Ricci almost solitons ⋮ Ricci solitons on almost Kenmotsu 3-manifolds ⋮ Gradient generalized \(\eta\)-Ricci soliton and contact geometry ⋮ Intrinsic and extrinsic geometry of hypersurfaces in \(\mathbb {S}^n \times \mathbb {R}\) and \(\mathbb {H}^n \times \mathbb {R}\) ⋮ Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces ⋮ Solitons on multiply warped product manifolds ⋮ Rigidity of gradient generalized \(\eta\)-Ricci solitons ⋮ Quasi-Einstein manifolds admitting a closed conformal vector field ⋮ Gradient Einstein solitons ⋮ A note on gradient solitons on two classes of almost Kenmotsu manifolds ⋮ Equivariant solutions to the optimal partition problem for the prescribed \(Q\)-curvature equation ⋮ Ricci solitons on locally conformally flat hypersurfaces in space forms ⋮ Soliton solutions for the Laplacian co-flow of some \(G_2\)-structures with symmetry ⋮ Rigidity of shrinking Ricci solitons ⋮ A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces ⋮ Homogeneous Ricci solitons are algebraic ⋮ Conformal Ricci solitons of Lagrangian submanifolds in K\"{a}hler manifolds ⋮ Solvsolitons associated with Heisenberg algebras ⋮ Stable and isoperimetric regions in some weighted manifolds with boundary ⋮ On semi-direct extensions of the Heisenberg group ⋮ Ricci Solitons on Multiply Warped Product Manifolds ⋮ Gradient ambient obstruction solitons on homogeneous manifolds ⋮ CLASSES OF GRADIENT RICCI SOLITONS ON GENERALIZED POINCARÉ MANIFOLDS ⋮ Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups ⋮ Conformally flat algebraic Ricci solitons on Lie groups ⋮ Seven dimensional cohomogeneity one manifolds with nonnegative curvature ⋮ Some triviality results for quasi-Einstein manifolds and Einstein warped products ⋮ ON NEW CLASSES OF EXPLICIT QUASI-EINSTEIN RIEMANNIAN MANIFOLDS ⋮ Initial value problem for cohomogeneity one gradient Ricci solitons ⋮ Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds ⋮ Vanishing results for the cotton tensor on gradient quasi-Einstein solitons ⋮ CONTACT GEOMETRY AND RICCI SOLITONS ⋮ On Ricci curvature of metric structures on \(\mathfrak{g}\)-manifolds ⋮ Ricci solitons on singly warped product manifolds and applications ⋮ Remarks on noncompact steady gradient Ricci solitons ⋮ Notes on contact Ricci solitons ⋮ Non-trivial \(m\)-quasi-Einstein metrics on simple Lie groups ⋮ Ricci soliton solvmanifolds ⋮ CLASSES OF GRADIENT RICCI SOLITONS ⋮ Ricci solitons of compact real hypersurfaces in Kähler manifolds ⋮ Unnamed Item ⋮ Locally homogeneous non-gradient quasi-Einstein 3-manifolds ⋮ Unnamed Item ⋮ On the Ricci curvature of steady gradient Ricci solitons ⋮ Estimates for the eigenvalues of the bi-drifting Laplacian on cigar soliton ⋮ SOME GEOMETRIC ANALYSIS ON GENERIC RICCI SOLITONS ⋮ Optimal Curvature Estimates for Homogeneous Ricci Flows ⋮ Chern-Yamabe problem and Chern-Yamabe soliton ⋮ Unnamed Item ⋮ Four-dimensional pseudo-Riemannian homogeneous Ricci solitons ⋮ On the Ricci flow of homogeneous metrics on spheres

Cites Work