Paper · Jun 26, 2017
A new approach to gradient Ricci solitons and generalizations
As on arXiv
Abstract
This short note concerns with two inequalities in the geometry of gradient Ricci solitons on a smooth manifold . These inequalities provide some relationships between the curvature of the Riemannian metric and the behavior of the scalar field through two second order equations satisfied by the scalar . We propose several generalizations of Ricci solitons to the setting of manifolds endowed with linear connections, not necessary of metric type.
- Submitted
- Jun 26, 2017
- Last revised
- Jul 10, 2017 (v4)
- Subjects
- math.DG
Comments: revised and expanded version
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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.