Closed $G$-structures defined by three-webs

M. A. Akivis, A. M. Shelekhov<sup>a

a</sup> Tver State University

Abstract: 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.

UDC: 514.763.7

Received: 19.06.2011