Generalised Kähler structure on $  \mathbb{C}P^2 $ and elliptic functions

Francesco Bonechi; Jian Qiu; Marco Tarlini; Francesco Bonechi; Jian Qiu; Marco Tarlini

doi:10.3934/jgm.2023009

Journal of Geometric Mechanics

2023, Volume 15, Issue 1: 188-223. doi: 10.3934/jgm.2023009

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Research article

Generalised Kähler structure on $ \mathbb{C}P^2 $ and elliptic functions

1.
INFN Sezione di Firenze, Italy
2.
Matematiska institutionen, Institutionen för fysik och astronomi, Uppsala Universitet, Sweeden

Received: 21 December 2021 Revised: 01 September 2022 Accepted: 04 October 2022 Published: 02 February 2023
Primary: 53D18; Secondary: 53D17, 53C15

We construct a toric generalised Kähler structure on $ \mathbb{C}P^2 $ and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised Kähler potential in terms of integrals of elliptic functions.
Citation: Francesco Bonechi, Jian Qiu, Marco Tarlini. Generalised Kähler structure on $ \mathbb{C}P^2 $ and elliptic functions[J]. Journal of Geometric Mechanics, 2023, 15(1): 188-223. doi: 10.3934/jgm.2023009

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Abstract

We construct a toric generalised Kähler structure on $ \mathbb{C}P^2 $ and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised Kähler potential in terms of integrals of elliptic functions.

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