On Einstein Manifolds of Positive Sectional Curvature

1998/07/11 by Matthew J. Gursky, Matthew Gursky, Claude LeBrun +2 · 4 citations
Mathematics · Physics and Astronomy · #53C21 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C21

paper · pdf · doi:10.48550/arxiv.math/9807055

14 pages, LaTeX2e

arxiv created 1998/07/11 · openalex publication_date 1998/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a compact oriented Einstein 4-manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M,g) is CP2, equipped with its standard Fubini-Study metric.

Cited by

• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
• Some geometric properties of generalized φ-vacuum static spaces
• A note on Einstein metrics and Riemannian twistor spaces
• Some isolation and stability results for Einstein manifolds

Related

• Einstein Hermitian Metrics of Non Negative Sectional Curvature
• Four-dimensional Einstein manifolds with sectional curvature bounded from above
• Einstein 4-Manifolds and Nonpositive Isotropic Curvature
• 4-dimensional Riemannian manifolds with a harmonic 2-form of constant length
• Toric Einstein 4-manifolds with nonnegative sectional curvature