Generalised K\"ahler Structure on $\mathbb{C}P^2$ and Elliptic Functions

Abstract

We construct a toric generalised K\"ahler 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 K\"ahler potential in terms of integrals of elliptic functions.