Geodesic
Geometric classification of orbits of a family of Killing vector fields in Euclidean spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 56-61

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Let $D \subset V(M) $ be a family of smooth vector fields defined on a manifold $M$. We examine properties of orbits of a family of Killing vector fields in Euclidean spaces and prove the existence of two Killing vector fields in Euclidean spaces such that the orbit of a family consisting of these vector fields covers the whole Euclidean space. A classification of orbits of Killing vector fields in Euclidean spaces is given.
Keywords: smooth manifold, Killing vector field, Lie algebra, Lie bracket, controllability.
Mots-clés : orbit 
@article{INTO_2021_197_a5,
     author = {S. S. Saitova},
     title = {Geometric classification of orbits of a family of {Killing} vector fields in {Euclidean} spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {56--61},
     publisher = {mathdoc},
     volume = {197},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_197_a5/}
}
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S. S. Saitova. Geometric classification of orbits of a family of Killing vector fields in Euclidean spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 56-61. http://geodesic.mathdoc.fr/item/INTO_2021_197_a5/