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July, 2021 Deformation for coupled Kähler–Einstein metrics
Satoshi NAKAMURA
Author Affiliations +
J. Math. Soc. Japan 73(3): 933-947 (July, 2021). DOI: 10.2969/jmsj/84408440

Abstract

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.

Funding Statement

The author is partly supported by Grant-in-Aid for JSPS Fellowships for Young Scientists No.17J02783 and No.19J01482.

Citation

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Satoshi NAKAMURA. "Deformation for coupled Kähler–Einstein metrics." J. Math. Soc. Japan 73 (3) 933 - 947, July, 2021. https://doi.org/10.2969/jmsj/84408440

Information

Received: 9 March 2020; Published: July, 2021
First available in Project Euclid: 26 May 2021

Digital Object Identifier: 10.2969/jmsj/84408440

Subjects:
Primary: 53C25
Secondary: 53C55, 58E11

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 3 • July, 2021
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