Bach-pinched metrics on closed manifolds

2025/05/19 by Letizia Branca, Giovanni Catino, Branca, Letizia +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2505.13059

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Exploiting the deformation method introduced by Aubin in his seminal work to construct constant negative scalar curvature metrics, we show the existence, on every closed manifold of dimension four, of a metric whose Bach tensor is pinched by the scalar curvature.

Citations

• Rigidity of Einstein manifolds with positive Yamabe invariant
• Some canonical metrics \em via Aubin's local deformations
• Metrics of constant negative scalar-Weyl curvature
• Four dimensional closed manifolds admit a weak harmonic Weyl metric
• Critical metrics on connected sums of Einstein four-manifolds
• On Bach-flat gradient shrinking Ricci solitons
• A note on negative isotropic curvature
• A conformally invariant sphere theorem in four dimensions
• On Einstein Manifolds of Positive Sectional Curvature
• Yamabe Invariants and Spin^c Structures
• Kodaira Dimension and the Yamabe Problem

Related

• Metrics of constant negative scalar-Weyl curvature
• Some canonical metrics \em via Aubin's local deformations
• New Rigidity Results for Critical Metrics of Some Quadratic Curvature Functionals
• Kähler manifolds with an almost 1/4-pinched metric
• Rigidity of the total scalar curvature with divergence-free Bach tensor