Geodesic
On the construction of unit longitudinal-vortex vector fields with the use of smooth mappings
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 82-91

Voir la notice de l'article provenant de la source Math-Net.Ru

A solution is given for the problem of constructing a unit vector field collinear to the field of its curl. The solution is based on the use of a suitably parametrized orthogonal transformation of a unit vector field that is potential in $\mathbb R^3$. The result is stated in the theorem that contains the recipe for constructing the required field. 
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V. P. Vereshchagin; Yu. N. Subbotin; N. I. Chernykh. On the construction of unit longitudinal-vortex vector fields with the use of smooth mappings. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 82-91. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a6/