当前位置: X-MOL 学术Comm. Pure Appl. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Classification of Generalized Kähler‐Ricci Solitons on Complex Surfaces
Communications on Pure and Applied Mathematics ( IF 3 ) Pub Date : 2020-09-30 , DOI: 10.1002/cpa.21947
Jeffrey Streets 1 , Yury Ustinovskiy 2
Affiliation  

Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that these solitons are generalized Kahler in two distinct ways, with vanishing and nonvanishing Poisson structure. This gives the first examples of generalized Kahler structures with nonvanishing Poisson structure on non-standard Hopf surfaces, completing the existence question for such structures. Moreover this gives a complete answer to the existence question for generalized Kahler-Ricci solitons on compact complex surfaces. In the setting of generalized Kahler geometry with vanishing Poisson structure, we show that these solitons are unique. We show that these solitons are global attractors for the generalized Kahler-Ricci flow among metrics with maximal symmetry.

中文翻译:

复杂表面上广义 Kähler-Ricci 孤子的分类

使用复曲面几何,我们给出了首先在 arXiv:1802.00170 中构建的多封闭流的紧凑稳定孤子的明确构造。这种构造还揭示了这些孤子以两种不同的方式被概括为 Kahler,具有消失和非消失泊松结构。这给出了在非标准 Hopf 表面上具有非零泊松结构的广义 Kahler 结构的第一个例子,完成了此类结构的存在性问题。此外,这给出了紧复曲面上广义 Kahler-Ricci 孤子的存在问题的完整答案。在具有消失泊松结构的广义 Kahler 几何的设置中,我们证明这些孤子是独一无二的。我们表明,这些孤子是具有最大对称性的度量之间的广义 Kahler-Ricci 流的全局吸引子。
更新日期:2020-09-30
down
wechat
bug