Geodesic
An example of a~Carnot manifold with $C^1$-smooth basis vector fields
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 84-87

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In this paper we construct an example of a Carnot manifold whose basis vector fields are of class $C^1$ but not of class $C^2$.
Keywords: Carnot manifold, commutator of vector fields. 
@article{IVM_2011_5_a11,
     author = {M. B. Karmanova},
     title = {An example of {a~Carnot} manifold with $C^1$-smooth basis vector fields},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {84--87},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_5_a11/}
}
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M. B. Karmanova. An example of a~Carnot manifold with $C^1$-smooth basis vector fields. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 84-87. http://geodesic.mathdoc.fr/item/IVM_2011_5_a11/