As on arXiv
Abstract
In the present work we find the Lie point symmetries of the Ricci flow on an -dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations – seen as a "static" Ricci flow – , and of some particular types of metrics of interest, such as, on warped products of manifolds. Finally, we use the symmetries found to obtain invariant solutions of the Ricci flow for the particular families of metrics considered.
- Submitted
- Dec 27, 2022
- Last revised
- Jan 15, 2023 (v2)
- Subjects
- math.DG, math.AP
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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
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 10A.12Curve Shortening and Minimal Discs
How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.
- 11A.1The Equation and Its First Solutions
A heat equation for the metric: spheres, cylinders and scaling.