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Transport net

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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

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


Comments

References

[a1] W. Blaschke, "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , 2 , Springer (1923)
How to Cite This Entry:
Transport net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transport_net&oldid=32083
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article