As on arXiv
Abstract
There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group , or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra , denoted by , , and . We show that, in a specific case, is an algebraic Ricci soliton that is shrinking. Moreover, is an algebraic Ricci soliton only on the three-dimensional Heisenberg Lie algebra and it is shrinking. Finally, we show that is a steady algebraic Ricci soliton on for . However, for , is flat.
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups
Topics Physics, Ricci solitons · Same author Youssef Ayad · Shared terms “algebraic Ricci”, “Lorentzian”, “Lie”
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Four-dimensional Lorentzian algebraic Ricci solitons
Topics Physics, Ricci solitons · Shared terms “Lorentzian algebraic”, “algebraic Ricci”, “left invariant”
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Topics Ricci solitons · Same author Youssef Ayad · Shared terms “algebraic Ricci”, “Lie algebras”, “inner product”
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Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”, “left invariant”, “algebraic”
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Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”
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Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”, “Lie”
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Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group
Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”, “Lie”
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Lorentz Ricci solitons of 4-dimensional non-Abelian nilpotent Lie groups
Topics Physics, Ricci solitons · Shared terms “invariant Lorentzian”, “Lorentzian metrics”, “left invariant”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 10A.1A Zoo of Three-Manifolds
The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.
- 10A.2Finite Rotation Groups and Spherical Space Forms
Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.
- 10A.4Homotopy Groups, Degree and the Hurewicz Theorem
Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.