Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups
Copyright policy )Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups
We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons. We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are solvsolitons. In particular, we obtain new solitons on $G_{2}$, $G_{5}$, and $G_{6}$, and we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.
30 pages
- Polytechnic School of Algiers Algeria
- École Normale Supérieure France
- Shumei University Japan
Mathematics - Differential Geometry, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), 53C50, 53C21, 53C25, left-invariant metrics, algebraic Ricci solitons, FOS: Mathematics, Lorentzian Lie groups, Methods of global Riemannian geometry, including PDE methods; curvature restrictions
Mathematics - Differential Geometry, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), 53C50, 53C21, 53C25, left-invariant metrics, algebraic Ricci solitons, FOS: Mathematics, Lorentzian Lie groups, Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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