Difference between revisions of "Transport net"
From Encyclopedia of Mathematics
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A conjugate [[Chebyshev net|Chebyshev net]] on a two-dimensional surface in an affine (or Euclidean) space. A surface carrying a transport net is called a [[Translation surface|translation surface]]. | A conjugate [[Chebyshev net|Chebyshev net]] on a two-dimensional surface in an affine (or Euclidean) space. A surface carrying a transport net is called a [[Translation surface|translation surface]]. | ||
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| − | <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> |
| − | + | <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> | |
| − | + | <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> | |
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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=11356
Transport net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transport_net&oldid=11356
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article