Premium
Classification of Generalized Kähler‐Ricci Solitons on Complex Surfaces
Author(s) -
Streets Jeffrey,
Ustinovskiy Yury
Publication year - 2021
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21947
Subject(s) - mathematics , ricci flow , poisson distribution , attractor , flow (mathematics) , symmetry (geometry) , pure mathematics , mathematical analysis , mathematical physics , geometry , ricci curvature , statistics , curvature
Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in by the first author in 2019. This construction also reveals that these solitons are generalized Kähler in two distinct ways, with vanishing and nonvanishing Poisson structure. This gives the first examples of generalized Kähler structures with nonvanishing Poisson structure on nonstandard Hopf surfaces, completing the existence question for such structures. Moreover, this gives a complete answer to the existence question for generalized Kähler‐Ricci solitons on compact complex surfaces. In the setting of generalized Kähler geometry with vanishing Poisson structure, we show that these solitons are unique. We show that these solitons are global attractors for the generalized Kähler‐Ricci flow among metrics with maximal symmetry. © 2020 Wiley Periodicals LLC