Geodesic
A lemma on Lie bracket under insufficient smoothness
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 73-77

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

Let two vector fields on a $C^2$-variety $M$ be tangent to a $C^1$-submanifold $F\subset M$. We show if that these fields are differentiable at a point $p\in F$, then their Lie bracket is also tangent to $F$. This statement is a weakening of the “easy part” assumptions of the Frobenius theorem.
Keywords: Lie bracket. 
K. V. Storozhuk. A lemma on Lie bracket under insufficient smoothness. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 73-77. http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a5/
@article{VNGU_2017_17_1_a5,
     author = {K. V. Storozhuk},
     title = {A lemma on {Lie} bracket under insufficient smoothness},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {73--77},
     year = {2017},
     volume = {17},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a5/}
}
TY  - JOUR
AU  - K. V. Storozhuk
TI  - A lemma on Lie bracket under insufficient smoothness
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2017
SP  - 73
EP  - 77
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a5/
LA  - ru
ID  - VNGU_2017_17_1_a5
ER  - 
%0 Journal Article
%A K. V. Storozhuk
%T A lemma on Lie bracket under insufficient smoothness
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2017
%P 73-77
%V 17
%N 1
%U http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a5/
%G ru
%F VNGU_2017_17_1_a5

[1] Dieudonné J., Treatise on Analysis, v. 3, Academic Press, New York, 1972 | MR | Zbl

[2] S. Kobayashi, K. Nomizu, Foundations of differential geometry, v. I, Interscience Publishers, a division of John Wiley Sons, New York–London, 1963 | MR | Zbl

[3] Stefan P., “Accessible Sets, Orbits, and Foliations with Singularities”, Proc. London Math. Soc., 3:29 (1974), 699–713 | DOI | MR | Zbl

[4] K. V. Storozhuk, “The Caratheodory–Rashevsky–Chow theorem for the nonholonomic Lipschitz distributions”, Sib. Math. J., 54:6 (2013), 1098–1103 | DOI | MR | Zbl

[5] I. A. Shvedov, Compact Course in Mathematical Analysis, v. 2, Function of Many Variables, Novosibirsk, 2003