Toric generalized Kaehler structures. III

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.

arXiv commentA continuation of the preprints arXiv:1810.08265v1 and arXiv:1811.06848v1. 38 pages

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Cited by in corpus (2)

• Differential calculus for generalized geometry and geometric Lax flows
• Matsushima-Lichnerowicz type theorems of Lie algebra of automorphisms of generalized Kähler manifolds of symplectic type