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There are significant differences between Helmholtz and Hodge's decompositiontheorems, but both share a common flavor. This paper is a first step to bringthem together.  We here produce Helmholtz theorems for differential 1-forms and 2-forms in3-D Euclidean space. We emphasize their common structure in order to facilitatethe understanding of another paper, soon to be made public, where a Helmholtztheorem for arbitrary differential forms in arbitrary Euclidean space ispresented and which allows one to connect (actually to derive from it) animprovement of Hodge's decomposition theorem.

Helmholtz Theorem for Differential Forms in 3-D Euclidean Space