Formal structure of scalar curvature in generalized Kähler geometry
Year: 2026
Type: article
Abstract: Building on works of Boulanger [J. Symplectic Geom. 17 (2019), pp. 973–1019] and Goto [arXiv:2105.13654, 2021; and J. Symplectic Geom. 18 (2020), pp. 147–190], we show that Goto’s scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant algebroid, constrained by the choice of an adapted volume form. We derive an explicit formula for Goto’s scalar curvature, and show that it is constant for generalized Kähler-Ricci solitons. Restricting to the generically symplectic type case, we realize the generalized Kähler class as the complexified orbit of the Hamiltonian action above. This leads to a natural extension of Mabuchi’s metric and K K -energy, implying a conditional uniqueness result. Finally, in this setting we derive a Calabi-Matsushima-Lichnerowicz obstruction and a Futaki invariant.
DOI: 10.1090/cams/66
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7147266606