Rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature
Haiping Fu, Jianke Peng
TL;DR
This paper establishes rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature, demonstrating conditions under which these manifolds exhibit specific geometric properties, with some conditions proven to be optimal.
Contribution
The paper introduces new rigidity theorems for Bach-flat manifolds with positive scalar curvature, including sharp conditions that characterize their geometric structure.
Findings
Rigidity theorems for Bach-flat manifolds with positive scalar curvature
Conditions proven to be sharp for certain geometric properties
Enhanced understanding of the structure of such manifolds
Abstract
In this paper, we prove some rigidity theorems for compact Bach-flat -manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 1.4 have the additional properties of being sharp.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology