As on arXiv
Abstract
We construct an explicit two-parameter family of complete, non-compact, three-dimensional, smooth steady gradient generalized Ricci solitons with symmetry, providing a cylindrical counterpart to the spherically symmetric solitons recently found by Podestà and Raffero. The family is parametrized by a flux constant and a conserved quantity . For , the asymptotic geometry exhibits power-law decay; for , the metric converges exponentially fast to a flat cylinder of finite radius.
Comments: 20 pages. This work is part of the author's PhD thesis
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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.