Three-dimensional Lorentzian homogeneous Ricci solitons

2009/11/06 by Miguel Brozos‐Vázquez, Giovanni Calvaruso, Brozos-Vazquez, M. +5 · 3 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0911.1247

Abstract

We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing that all types (i.e. shrinking, expanding and steady) exist. Moreover, all non-trivial examples have non-diagonalizable Ricci operator with one only eigenvalue.

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• Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group
• Almost Ricci Solitons on Class \mathcal A Hypersurfaces of Product Spaces
• Ricci Solitons on a family of three dimensional Lorentzian Walker manifolds

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