Paper · Jul 4, 2023
Vanishing bach-like tensors on complete gradient shrinking ricci solitons
As on arXiv
Abstract
The Bach tensor is classically defined in dimension 4, and work from J. Bergman and others shows that where and are more basic 2-tensors, which are symmetric, divergence-free, algebraically independent, and quadratic in the Riemann tensor. In this paper, we extend H.-D. Cao and Q. Chen's results for Bach-flat gradient shrinking Ricci solitons to solitons with .
- Submitted
- Jul 4, 2023
- Subjects
- math.DG
Comments: 19 Pages, 1 Figure
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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.