The notion of coupled Kähler–Einstein metrics was introduced recently by Hultgren–Witt Nyström. In this paper we discuss deformation of a coupled Kähler–Einstein metric on a Fano manifold. 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.
The author is partly supported by Grant-in-Aid for JSPS Fellowships for Young Scientists No.17J02783 and No.19J01482.
"Deformation for coupled Kähler–Einstein metrics." J. Math. Soc. Japan 73 (3) 933 - 947, July, 2021. https://doi.org/10.2969/jmsj/84408440