Harland, D orcid.org/0000-0002-4110-9673 (2023) Approximating the parallel transport of an induced connection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479 (2273). 20220761. ISSN 1364-5021
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 trivialization of the sub-bundle. The methods were developed 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Ⓒ 2023 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | induced connection; skyrmions; instantons |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Apr 2023 09:26 |
Last Modified: | 11 May 2023 23:43 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rspa.2022.0761 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198266 |