Helmholtz Theorem for Differential Forms in 3-D Euclidean Space
General Mathematics
2014-04-22 v2
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.
Cite
@article{arxiv.1404.3679,
title = {Helmholtz Theorem for Differential Forms in 3-D Euclidean Space},
author = {Jose G. Vargas},
journal= {arXiv preprint arXiv:1404.3679},
year = {2014}
}