Closed $G$-structures defined by three-webs
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 22-28
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We introduce the notion of $1$-digit identity of order $k$ and prove the theorem: if in coordinate loops of analytic three-web $W$ there hold $k-1$ independent identities of order $k$, $G$-structure defined by this web is a closed structure of class not higher than $2k$.
Keywords:
multidimensional three-web, closed $G$-structure, coordinate loop of a three-web, $1$-digit identity of $k$-th order.
@article{UZKU_2011_153_3_a1,
author = {M. A. Akivis and A. M. Shelekhov},
title = {Closed $G$-structures defined by three-webs},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {22--28},
publisher = {mathdoc},
volume = {153},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a1/}
}
TY - JOUR AU - M. A. Akivis AU - A. M. Shelekhov TI - Closed $G$-structures defined by three-webs JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2011 SP - 22 EP - 28 VL - 153 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a1/ LA - ru ID - UZKU_2011_153_3_a1 ER -
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M. A. Akivis; A. M. Shelekhov. Closed $G$-structures defined by three-webs. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 22-28. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a1/