# Toric generalized Kaehler structures. III

## TL;DR

This paper resolves a key open problem in generalized Kähler geometry by relating scalar curvature definitions directly to biHermitian structures, with applications to toric GK geometry of symplectic type.

## Contribution

It provides a direct link between scalar curvature in GK geometry and biHermitian structures, solving an open problem and confirming the scalar curvature definition in toric GK geometry.

## Key findings

- Scalar curvature in GK geometry is directly related to biHermitian structures.
- The paper confirms the scalar curvature in toric GK geometry matches Goto's definition.
- Resolved an open problem posed by R. Goto regarding scalar curvature in GK geometry.

## Abstract

The paper clarifies some subtle points surrounding the definition of scalar curvature in generalized K$\ddot{a}$hler (GK) geometry. We have solved an open problem in GK geometry of symplectic type posed by R. Goto \cite{Go1} on relating the scalar curvature defined in terms of generalized pure spinors \emph{directly} to the underlying biHermitian structure. In particular, we apply this solution to toric GK geometry of symplectic type and prove that the scalar curvature suggested in this setting by L. Boulanger \cite{Bou} coincides with Goto's definition.