Geodesic
Nonholonomic $(n+1)$-webs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 27-36 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On an $n$-manifold $M$ we consider nonholonomic $(n+1)$-web $NW$, which consists of $n+1$ distributions of codimension 1. We prove that the web $NW$ is equivalent to $G$-structure with structure group $\lambda E$, the group of scalar matrices. We obtain structure equations of the nonholonomic web $NW$ and find the integrability conditions of all its distributions. We show that a connection $\Gamma$ arises on the manifold $M$ carrying the web $NW$. Distributions of the web $NW$ are totally geodesic with respect to this connection. We consider the special case when the curvature of $\Gamma$ equals zero and in particular when the $(n+1)$-web $NW$ is formed by invariant distributions on the Lie group. We find the equations of the group when all distributions of $NW$ are integrable.
Keywords: nonholonomic $(n+1)$-web, $(n+1)$-web
Mots-clés : $G$-structure, $\lambda E$-structure. 
@article{IVM_2014_12_a2,
     author = {M. I. Kabanova and A. M. Shelekhov},
     title = {Nonholonomic $(n+1)$-webs},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--36},
     year = {2014},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_12_a2/}
}
TY  - JOUR
AU  - M. I. Kabanova
AU  - A. M. Shelekhov
TI  - Nonholonomic $(n+1)$-webs
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 27
EP  - 36
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_12_a2/
LA  - ru
ID  - IVM_2014_12_a2
ER  - 
%0 Journal Article
%A M. I. Kabanova
%A A. M. Shelekhov
%T Nonholonomic $(n+1)$-webs
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 27-36
%N 12
%U http://geodesic.mathdoc.fr/item/IVM_2014_12_a2/
%G ru
%F IVM_2014_12_a2
M. I. Kabanova; A. M. Shelekhov. Nonholonomic $(n+1)$-webs. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 27-36. http://geodesic.mathdoc.fr/item/IVM_2014_12_a2/

[1] Goldberg V. V., Theory of multicodimensional $(n+1)$-webs, Kluwer Academic Publ., Dordrecht–Boston, 1988 | MR | Zbl

[2] Kabanova M. I., “$\lambda E$-struktury”, Tr. mezhdunarodn. geometr. tsentra, 5:1 (2012), 25–30

[3] Sternberg S., Lektsii po differentsialnoi geometrii, Mir, M., 1970 | MR | Zbl

[4] Laptev G. F., “Osnovnye infinitezimalnye struktury vysshikh poryadkov na gladkom mnogoobrazii”, Tr. geom. semin., 1, 1966, 139–189 | MR | Zbl

[5] Kartan E., Prostranstva affinnoi, proektivnoi i konformnoi svyaznosti, Izd-vo Kazansk. un-ta, Kazan, 1962 | MR

[6] Vasileva M. V., Gruppy Li preobrazovanii, MGPI, M., 1969 | MR

[7] Voskanyan V. K., “O konformnoi strukture, prisoedinennoi k krivolineinoi $(n+1)$-tkani”, Problemy teorii tkanei i kvazigrupp, Kalininskii gos. un-t, Kalinin, 1985, 33–38 | MR | Zbl

[8] Voskanyan V. K., “Krivolineinye $(n+1)$-tkani na mnogoobrazii $M^n$”, Matematika, 3, Erevanskii un-t, Erevan, 1985, 163–175 | MR