Chebyshev net
From Encyclopedia of Mathematics
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 Δin−1(x)⊂Δin−1 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
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