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 
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/
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Voir la notice du chapitre de livre 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.

[1] Vereschagin V. P., Subbotin Yu. N., Chernykh N. I., “Sposob postroeniya vektornykh polei s opredelennymi vikhrevymi svoistvami s pomoschyu gladkikh otobrazhenii”, Materialy Ufim. mezhdunar. mat. konf., posvyaschennoi pamyati A. F. Leonteva, T. 1, IMVTs, Ufa, 2007, 48–49

[2] Aminov Yu. A., Geometriya vektornogo polya, Nauka, M., 1990, 208 pp. | MR

[3] Nikolskii S. M., Kurs matematicheskogo analiza: uch. dlya fiz.-mat. spets. vuzov, 4-e izd., pererab. i dop. T. 1, Nauka, M., 1990, 528 pp. | MR