Transport net

A conjugate Chebyshev net on a two-dimensional surface in an affine (or Euclidean) space. A surface carrying a transport net is called a translation surface.

For transport nets one has Lie's theorem: If a surface carries two transport nets, then the tangents to the lines in these nets intersect on a non-singular plane curve of order four [1].

#### References[edit]

[1] |  V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)

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[a1] |  W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , 2 , Springer (1923)