Difference between revisions of "Chebyshev net"
From Encyclopedia of Mathematics
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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 | + | {{TEX|done}} |
| + | 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 $\Sigma_n$ such that, for each $i=1,\dots,n$, the directions of the distribution $\Delta_1^i(x)$ are parallel in the connection $\nabla$ along any integral curve of any of the other distributions $\Delta_1^i$ defined by this net. A Chebyshev net of the second kind is a net $\sigma_n$ ($n>2$) such that for each $i=1,\dots,n$, the subspaces $\Delta_{n-1}^i(x)\subset\Delta_{n-1}^i$ are parallel in the connection $\nabla$ along the integral curves of the distribution $\Delta_1^i$. | ||
Introduced by P.L. Chebyshev (1878). | Introduced by P.L. Chebyshev (1878). | ||
Revision as of 17:34, 22 August 2014
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 $\Sigma_n$ such that, for each $i=1,\dots,n$, the directions of the distribution $\Delta_1^i(x)$ are parallel in the connection $\nabla$ along any integral curve of any of the other distributions $\Delta_1^i$ defined by this net. A Chebyshev net of the second kind is a net $\sigma_n$ ($n>2$) such that for each $i=1,\dots,n$, the subspaces $\Delta_{n-1}^i(x)\subset\Delta_{n-1}^i$ are parallel in the connection $\nabla$ along the integral curves of the distribution $\Delta_1^i$.
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=17668
Chebyshev net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_net&oldid=17668
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article