Can I read Formal structure of scalar curvature in generalized K\"ahler geometry on EtoBox?

Formal structure of scalar curvature in generalized K\"ahler geometry by Apostolov, Vestislav; Streets, Jeffrey; Ustinovskiy, Yury is a scholarly article available to read on EtoBox.

What is Formal structure of scalar curvature in generalized K\"ahler geometry about?

Building on works of Boulanger and Goto, 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 K\"ahler-Ricci solitons. Restricting to the generically symplectic type case, we realize the generalized K\"ahler class as the complexified orbit of the Hamiltonian action above. This leads to a natural extension of Mabuchi's metric and $K$-energy, implying a conditional uniqueness result. Finally, in this setting we derive a Calabi-Matsushima-Lichnerowicz obstruction and a Futaki invariant.

Author

Apostolov, Vestislav; Streets, Jeffrey; Ustinovskiy, Yury

Published

2024

Language

EN