Deformation for coupled Kaehler-Einstein metrics

摘要

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