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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2011, Volume 153, Book 3, Pages 22–28 (Mi uzku1051)  

Closed $G$-structures defined by three-webs

M. A. Akivis, A. M. Shelekhova

a 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.

Full text: PDF file (203 kB)
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UDC: 514.763.7
Received: 19.06.2011

Citation: M. A. Akivis, A. M. Shelekhov, “Closed $G$-structures defined by three-webs”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153, no. 3, Kazan University, Kazan, 2011, 22–28

Citation in format AMSBIB
\Bibitem{AkiShe11}
\by M.~A.~Akivis, A.~M.~Shelekhov
\paper Closed $G$-structures defined by three-webs
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2011
\vol 153
\issue 3
\pages 22--28
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1051}


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