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

TL;DR

This paper constructs a toric generalized Kähler structure on complex projective space and expresses its geometric components using elliptic functions, providing explicit formulas for the potential.

Contribution

It introduces a novel construction of generalized Kähler structures on 2 using elliptic functions, linking complex geometry with special functions.

Findings

Explicit generalized Ke4hler structure on 2

Representation of structures via elliptic functions

Calculation of the Ke4hler potential through elliptic integrals

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.