Ricci solitons on Lorentzian-Walker three-manifolds

DOI10.1007/S10474-010-0049-ZzbMath1274.53100OpenAlexW2078177277MaRDI QIDQ653944

Barbara De Leo, Giovanni Calvaruso

Publication date: 20 December 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-010-0049-z

zbMATH Keywords

Lorentzian manifoldRicci solitonWalker structure

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (15)

On Lorentzian Ricci solitons on nilpotent Lie groups ⋮ Lorentz-conformal transformations in the plane ⋮ Four-dimensional Lorentzian Lie groups ⋮ Curvature properties and Ricci solitons of Lorentzian pr-waves manifolds ⋮ Generalized Ricci solitons on non-reductive four-dimensional homogeneous spaces ⋮ Affine generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated to Yano connection ⋮ Affine algebraic Ricci solitons associated to the Yano connections on three-dimensional Lorentzian Lie groups ⋮ Generalized Ricci solitons on three-dimensional Lorentzian Walker manifolds ⋮ Ricci solitons of the \(\mathbb{H}^2 \times \mathbb{R}\) Lie group ⋮ Ricci solitons on four-dimensional Lorentzian Walker manifolds ⋮ Ricci solitons on low-dimensional generalized symmetric spaces ⋮ Ricci and Yamabe solitons on second-order symmetric, and plane wave 4-dimensional Lorentzian manifolds ⋮ Unnamed Item ⋮ Ricci soliton vector fields of spherically symmetric static spacetimes ⋮ Four-dimensional pseudo-Riemannian homogeneous Ricci solitons

Cites Work

• On solutions of the Ricci curvature equation and the Einstein equation
• Nonlinear models in \(2+\epsilon\) dimensions
• Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
• Geometry of Ricci solitons
• Towards physically motivated proofs of the Poincaré and geometrization conjectures
• Ricci solitons and Einstein-scalar field theory
• Three-dimensional Lorentz manifolds admitting a parallel null vector field
• CANONICAL FORM FOR A RIEMANNIAN SPACE WITH A PARALLEL FIELD OF NULL PLANES

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