Inverting covariant exterior derivative
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912388151771136 |
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| author | Kycia, Radosław Antoni Šilhan, Josef |
| author_facet | Kycia, Radosław Antoni Šilhan, Josef |
| contents | The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some constraints that can fail, giving no solution, which is the expected case for parallel transport equations. These constraints are straightforward to obtain in the proposed approach. The relation to operational calculus and operator theory is outlined. The upshot of this paper is to show, using the linear homotopy operator of the Poincare lemma, that we can solve the covariant constant and related equations in a geometric and algorithmic way. The considerations related to the regularity of the solutions are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03663 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inverting covariant exterior derivative Kycia, Radosław Antoni Šilhan, Josef Differential Geometry Mathematical Physics Analysis of PDEs Operator Algebras 53-08, 53B05, 53Z05 The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some constraints that can fail, giving no solution, which is the expected case for parallel transport equations. These constraints are straightforward to obtain in the proposed approach. The relation to operational calculus and operator theory is outlined. The upshot of this paper is to show, using the linear homotopy operator of the Poincare lemma, that we can solve the covariant constant and related equations in a geometric and algorithmic way. The considerations related to the regularity of the solutions are provided. |
| title | Inverting covariant exterior derivative |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs Operator Algebras 53-08, 53B05, 53Z05 |
| url | https://arxiv.org/abs/2210.03663 |