Four-dimensional Lorentzian algebraic Ricci solitons
Eduardo Garcia-Rio, Rosalia Rodriguez-Gigirey, and Ramon Vazquez-Lorenzo
TL;DR
This paper classifies four-dimensional Lorentzian algebraic Ricci solitons, revealing that unlike the Riemannian case, every connected, simply connected four-dimensional Lie group admits a left-invariant Ricci soliton metric.
Contribution
It provides a complete description of four-dimensional Lorentzian algebraic Ricci solitons and highlights the contrast with Riemannian geometry.
Findings
Every connected, simply connected four-dimensional Lie group admits a left-invariant Ricci soliton.
The structure of Lorentzian Ricci solitons differs significantly from Riemannian cases.
The paper characterizes algebraic Ricci solitons in four-dimensional Lorentzian geometry.
Abstract
We describe four-dimensional Lorentzian algebraic Ricci solitons. In sharp contrast with the Riemannian situation, any connected and simply connected four-dimensional Lie group admits a left-invariant Lorentz metric which is a Ricci soliton.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Homotopy and Cohomology in Algebraic Topology