Deformation for coupled Kähler-Einstein metrics

Abstract

The notion of coupled Kähler-Einstein metrics was introduced recently by Hultgren-WittNyström. In this paper we discuss deformation of a coupled Kähler-Einstein metrics on a Fano manifold. In particular we obtain a necessary and sufficient condition for a coupled Kähler-Einstein metric to be deformed to another coupled Kähler-Einstein metric for a Fano manifold admitting non-trivial holomorphic vector fields. In addition we also discuss deformation for a coupled Käher-Einstein metric on a Fano manifold when the complex structure varies.

Some typos are fixed

References in corpus (2)

• Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
• Residue formula for an obstruction to Coupled Kähler-Einstein metrics