Complex structures on Einstein four-manifolds of positive scalar curvature

Abstract: The question that when a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, LeBrun classified Hermitian, Einstein four-manifolds of positive scalar curvature. In this talk we consider the inverse problem, that is, when a simply connected four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

2021 Pacific Rim Complex & Symplectic Geometry Conference