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Chebyshev net

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A net in which the tangent vectors to each family of lines can be parallel displaced along the lines of the other family. A Chebyshev net of the first kind is a net Σn such that, for each i=1,,n, the directions of the distribution Δi1(x) are parallel in the connection along any integral curve of any of the other distributions Δi1 defined by this net. A Chebyshev net of the second kind is a net Σn (n>2) such that for each i=1,,n, the subspaces Δin1(x)Δin1 are parallel in the connection along the integral curves of the distribution Δi1.

Introduced by P.L. Chebyshev (1878).

References

[1] P.L. Chebyshev, , Collected works , 5 , Moscow-Leningrad (1951) pp. 165–170 (In Russian)
How to Cite This Entry:
Chebyshev net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_net&oldid=33089
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article