论文标题
$ {\ mathbb r}^k $的音量保留动作的渐近链接
Asymptotic linking of volume-preserving actions of ${\mathbb R}^k$
论文作者
论文摘要
我们将V. Arnold的渐近线链接理论扩展到$ {\ Mathbb r}^3 $和$ s^3 $中的两个卷中的流量，以保留$ {\ Mathbb r}^k $ {\ Mathbb r}^k $和$ {\ Mathb r}^\ ell $ { $ {\ mathbb r}^k $，带有封闭式的单数$ \ ell $ -dimensional submanifold in $ {\ Mathbb r}^n $，其中$ n = k+\ ell+1 $。我们还将生物 - 萨瓦特公式扩展到更高的维度。
We extend V. Arnold's theory of asymptotic linking for two volume preserving flows on a domain in ${\mathbb R}^3$ and $S^3$ to volume preserving actions of ${\mathbb R}^k$ and ${\mathbb R}^\ell$ on certain domains in ${\mathbb R}^n$ and also to linking of a volume preserving action of ${\mathbb R}^k$ with a closed oriented singular $\ell$-dimensional submanifold in ${\mathbb R}^n$, where $n=k+\ell+1$. We also extend the Biot-Savart formula to higher dimensions.
