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arXiv · 1404.3679

Helmholtz Theorem for Differential Forms in 3-D Euclidean Space

Jose G. Vargas
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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.

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Jose G. Vargas. 2014-04-20. Helmholtz Theorem for Differential Forms in 3-D Euclidean Space. https://arxiv.org/abs/1404.3679

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