Approximating the parallel transport of an induced connection
arXiv:2204.04032 · doi:10.1098/rspa.2022.0761
Abstract
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.
17 pages