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arXiv · 2109.10295

Variational structure and uniqueness of generalized K\"ahler-Ricci solitons

Vestislav Apostolov·Jeffrey Streets·Yury Ustinovskiy
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Abstract

Under broad hypotheses we derive a scalar reduction of the generalized K\"ahler-Ricci soliton system. We realize solutions as critical points of a functional analogous to the classical Aubin energy defined on the orbit of a natural Hamiltonian action of diffeomorphisms, thought of as a generalized K\"ahler 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 K\"ahler class. As an application we prove uniqueness of the generalized K\"ahler-Ricci solitons on Hopf surfaces constructed in arXiv:1907.03819, finishing the classification in complex dimension $2$.

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Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy. 2021-09-21. Variational structure and uniqueness of generalized K\"ahler-Ricci solitons. https://arxiv.org/abs/2109.10295

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