Geodesic
On the factor-web $\overline W(\rho,r,r)$ of the three-web $W(r,r,r)$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 115-128.

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The notion of the factor-web $\overline W(\rho,r,r)$ ($1\leq\rho$) is defined for the three-web $W(r,r,r)$ formed on a $2r$-dimensional differentiable manifold by three $r$-dimensional smooth foliations. Embedding of the factor-web in the initial web $W(r,r,r)$ 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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G. A. Tolstikhina. On the factor-web $\overline W(\rho,r,r)$ of the three-web $W(r,r,r)$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 115-128. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a11/

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