论文标题
Kähler扭曲空间上的点涡流动力学
Point vortex dynamics on Kähler twistor spaces
论文作者
论文摘要
在本文中，我们提供工具来研究$ \ Mathbb {cp}^n $和flag歧管$ \ mathbb {f} _ {1,2}（\ mathbb {c}^3）$的点涡流动力学的动力学。这些是唯一由4个manifolds产生的Kähler扭曲空间。我们在$ \ mathbb {cp}^n $上给出了Green功能的明确表达式，这使我们能够确定hamiltonian $ h $以及$ \ mathbb {cp}^n $的点涡流问题的动作方程。此外，我们确定动量映射$μ：\ mathbb {f} _ {1,2}（\ mathbb {c}^3）\ to \ mathfrak {su}^*（3）$ in Flag歧管上的$。
In this paper, we provide tools to study the dynamics of point vortex dynamics on $\mathbb{CP}^n$ and the flag manifold $\mathbb{F}_{1,2}(\mathbb{C}^3)$. These are the only Kähler twistor spaces arising from 4-manifolds. We give an explicit expression for Green's function on $\mathbb{CP}^n$ which enables us to determine the Hamiltonian $H$ and the equations of motions for the point vortex problem on $\mathbb{CP}^n$. Moreover, we determine the momentum map $μ:\mathbb{F}_{1,2}(\mathbb{C}^3)\to \mathfrak{su}^*(3)$ on the flag manifold.
