As on arXiv
Abstract
On an -dimensional complete manifold , consider an -almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and , then the manifold is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. Moreover, if the dimension of is four, the metric is conformally flat.
- Submitted
- Apr 14, 2016
- Last revised
- Oct 13, 2016 (v2)
- Subjects
- math.DG
- Journal
- Pacific J. Math. 288 (2017) 475-488
Comments: 12 pages
Its neighbourhood
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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
- 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.