Paper · Oct 14, 2025
Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
As on arXiv
Abstract
The objective of this paper is to deepen the study of vector fields on hyperbolic spaces that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions and . In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enrich the understanding of self-similar solutions of the Ricci flow in a more general context.
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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
- 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.