A note on the Hitchin-Thorpe inequality and Ricci flow on 4-manifolds
Yuguang Zhang, Zhenlei Zhang
TL;DR
This paper establishes a Hitchin-Thorpe type inequality for certain 4-manifolds with non-positive Yamabe invariant that admit long-term normalized Ricci flow solutions with bounded scalar curvature.
Contribution
It introduces a new inequality relating topology and geometric flow properties for 4-manifolds with specific curvature conditions.
Findings
Proves a Hitchin-Thorpe type inequality for these manifolds.
Shows the inequality holds under long-time Ricci flow with bounded scalar curvature.
Connects topological invariants with geometric flow behavior.
Abstract
In this short paper, we prove a Hitchin-Thorpe type inequality for closed 4-manifolds with non-positive Yamabe invariant, and admitting long time solutions of the normalized Ricci flow equation with bounded scalar curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology