(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 115-128

## On the factor-web $\bar W\left(\rho,r,r\right)$ of the three-web $W\left(r,r,r\right)$

G. A. Tolstikhina

Abstract

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The notion of the factor-web $\bar W\left(\rho,r,r\right)$ ($1$£ r < r) is defined for the three-web $W\left(r,r,r\right)$ formed on a $2r$-dimensional differentiable manifold by three $r$-dimensional smooth foliations. Embedding of the factor-web in the initial web $W\left(r,r,r\right)$ is constructed. This construction is a well-known geometric analog of the canonical extension of a Lie group of transformations to its parameter group.

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