Approximating the parallel transport of an induced connection

04/08/2022

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by   Derek Harland, et al.

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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.