Einstein Metrics, Conformal Curvature, and Anti-Holomorphic Involutions

TL;DR

This paper classifies all compact oriented Einstein 4-manifolds with positive determinant of the self-dual Weyl tensor, identifying exactly 15 such manifolds and their unique Einstein metric components.

Contribution

It completes the classification of these Einstein 4-manifolds, specifying their count and the structure of their moduli space.

Findings

Exactly 15 such manifolds exist up to diffeomorphism.

Each manifold has a unique connected component in the Einstein moduli space.

The classification builds on and completes previous partial results.

Abstract

Building on previous results, we complete the classification of compact oriented Einstein 4-manifolds with det (W^+) > 0. There are, up to diffeomorphism, exactly 15 manifolds that carry such metrics, and, on each of these manifolds, such metrics sweep out exactly one connected component of the corresponding Einstein moduli space.