Helmholtz Theorem for Differential Forms in 3-D Euclidean Space
Abstract
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and 2-forms in 3-D Euclidean space. We emphasize their common structure in order to facilitate the understanding of another paper, soon to be made public, where a Helmholtz theorem for arbitrary differential forms in arbitrary Euclidean space is presented and which allows one to connect (actually to derive from it) an improvement of Hodge's decomposition theorem.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2014
- DOI:
- 10.48550/arXiv.1404.3679
- arXiv:
- arXiv:1404.3679
- Bibcode:
- 2014arXiv1404.3679V
- Keywords:
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- Mathematics - General Mathematics