Geodesic
Geometry of orbits of vector fields
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 69-77

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In this paper, we study geometric and topological properties of vector fields on Riemannian manifolds of constant and nonnegative curvature, including Killing vector fields. We construct a completely integrable family of vector fields such that its orbits form a foliation whose set of singular fibers consists of two circles and regular fibers are two-dimensional tori. The solenoidal character of Killing vector fields on three-dimensional Euclidean space is also proved.
Keywords: vector field, Killing vector field, roughness of vector fields. 
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     author = {Zh. O. Aslonov},
     title = {Geometry of orbits of vector fields},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {69--77},
     publisher = {mathdoc},
     volume = {197},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_197_a7/}
}
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Zh. O. Aslonov. Geometry of orbits of vector fields. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 69-77. http://geodesic.mathdoc.fr/item/INTO_2021_197_a7/