Paper · Jan 30, 2020
Curvature estimates and gap theorems for expanding Ricci solitons
As on arXiv
Abstract
We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that the scalar curvature is non-negative and the potential function is proper. We also give an upper bound for the scalar curvature of noncompact expander when the Ricci curvature is nonpositive and the potential function is proper. We then provide a sufficient condition for the scalar curvature of expanding soliton being nonnegative. We also estimate the curvature of expanding soliton in dimensions three and four. As an application, we prove a gap theorem on three dimensional gradient expander.
- Submitted
- Jan 30, 2020
- Last revised
- Aug 13, 2021 (v2)
- Subjects
- math.DG
Comments: 33 pages. Theorem 6 improved
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Background reading
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In the guidebook
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The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.
- 10A.2Finite Rotation Groups and Spherical Space Forms
Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.
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