论文标题
近似诱导连接的平行传输
Approximating the parallel transport of an induced connection
论文作者
论文摘要
提出了有效的数值方法，以近似近似于向量束的子束上诱导连接的平行传输运算符。这些方法比runge-kutta算法的幼稚应用更简单，并且精确度为4。它们具有对子束琐事的选择不敏感的理想属性。开发了这些方法是为了解决使用Atiyah-Manton--Sutcliffe和Atiyah--drinfeld--Hitchin--Hitchin-Manin构建的问题，但适用于计算几何形状的更广泛问题。
Efficient numerical methods to approximate the parallel transport operators of the induced connection on a sub-bundle of a vector bundle are presented. These methods are simpler than naive applications of a Runge--Kutta algorithm, and have accuracy up to order 4. They have the desirable property of being insensitive to choices of trivialisation of the sub-bundle. The methods were developed in order to solve a problem of computing skyrmions using the Atiyah--Manton--Sutcliffe and Atiyah--Drinfeld--Hitchin--Manin constructions, but are applicable to a broader range of problems in computational geometry.
