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]]. | ||
Revision as of 15:55, 1 May 2014
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=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