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Difference between revisions of "Transport net"

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====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.I. Shulikovskii,  "Classical differential geometry in a tensor setting" , Moscow  (1963)  (In Russian)</TD></TR></table>
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<table>
 
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<TR><TD valign="top">[1]</TD> <TD valign="top">  V.I. Shulikovskii,  "Classical differential geometry in a tensor setting" , Moscow  (1963)  (In Russian)</TD></TR>
 
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Blaschke,  "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , '''2''' , Springer  (1923)</TD></TR>
 
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</table>
====Comments====
 
 
 
 
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Blaschke,  "Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Affine Differentialgeometrie" , '''2''' , Springer  (1923)</TD></TR></table>
 

Latest revision as of 08:49, 8 April 2023

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)
[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=53630
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article