Normal Forms and Einstein 4-manifolds

2025/08/11 by Aazami, Amir Babak · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.08118

Abstract

We find new examples of normal forms for oriented Riemannian 4-manifolds by generalizing the Hodge star-Einstein condition. These normal forms include curvature-distinguished metrics; they also generalize Berger's result on the nonnegativity of the Euler characteristic, as well as the Hitchin-Thorpe inequality.

Citations

• On the curvature operator in dimensions 4n
• Spin Manifolds, Einstein Metrics, and Differential Topology

Cited by

• On the curvature operator in dimensions 4n

Related

• Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds
• Einstein 4-Manifolds and Nonpositive Isotropic Curvature
• 4-Manifolds without Einstein Metrics
• Four-dimensional Einstein manifolds with sectional curvature bounded from above
• Monopole classes and Einstein metrics