Coupled Kähler-Einstein metrics

Abstract

We propose new types of canonical metrics on Kähler manifolds, called coupled Kähler-Einstein metrics, generalizing Kähler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is Kähler-Einstein Fano. In the Fano case we also prove that existence of coupled Kähler-Einstein metrics imply a certain algebraic stability condition, generalizing $K$-polystability.

18 pages

References in corpus (1)

• Kähler-Einstein metrics along the smooth continuity method