Differential Geometry Seminar | Formal structure of scalar curvature in generalized Kahler geometry

Abstract：

The Fujiki-Donaldson moment map formulation of scalar curvature problem, and the attendant Mabuchi-Semmes-Donaldson geometry of a Kahler class, play a central role in addressing the existence and uniqueness of constant scalar curvature Kahler metrics. Generalized Kahler (GK) geometry is a natural extension of Kahler geometry arising from Hitchin’s generalized geometry program and mathematical physics, and forms a particularly well-structured extension of Kahler geometry. Recently Goto defined a notion of scalar curvature in GK geometry as the moment map of a particular Hamiltonian action on the space of generalized Kahler structures. In this talk I will describe joint work with Vestislav Apostolov and Yury Ustinovskiy where we give an explicit description of the scalar curvature, and define a natural generalization of the Mabuchi-Semmes-Donaldson metric, leading to a Calabi-Lichnerowicz-Matsushima obstruction, generalizations of Futaki’s invariants, and a conditional uniqueness result.