Paper · Jun 18, 2024
On some -dimensional almost -Ricci solitons with diagonal metrics
As on arXiv
Abstract
We study some properties of a -dimensional manifold with a diagonal Riemannian metric as an almost -Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if is given; we get constraints on the metric when the potential vector field has a particular expression; we compute the defining functions of the soliton when both the potential vector field and the -form are prescribed. Moreover, we find conditions for the manifold to be flat. Based on the theoretical results, we provide examples.
Comments: 38 pages
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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
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.