Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orb...Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.展开更多
基金V.A.was supported in part by an NSERC Discovery Grant and a Connect Talent Grant of the Région Pays de la Loire.
文摘Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.
