Geodesic
Nonholonomic $(n+1)$-webs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 27-36

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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},
     publisher = {mathdoc},
     number = {12},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_12_a2/}
}
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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/