Chebyshev net

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)