An upper diameter bound for compact Ricci solitons with applications to the Hitchin-Thorpe inequality
Homare Tadano
TL;DR
This paper establishes an upper bound on the diameter of compact Ricci solitons based on scalar curvature range and applies this to derive conditions under which four-dimensional Ricci solitons satisfy the Hitchin-Thorpe inequality.
Contribution
It introduces a new diameter bound for compact Ricci solitons related to scalar curvature and applies it to the Hitchin-Thorpe inequality in four dimensions.
Findings
Upper diameter bound in terms of scalar curvature range
Sufficient conditions for Hitchin-Thorpe inequality in four dimensions
Extension of previous results by Fernandez-Lopez and Garcia-Rio
Abstract
In this article, stimulated by Fernandez-Lopez and Garcia-Rio, we shall give an upper diameter bound for compact Ricci solitons in terms of the range of the scalar curvature. As an application, we shall provide some sufficient conditions for four-dimensional compact Ricci solitons to satisfy the Hitchin-Thorpe inequality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities