Voss net

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A conjugate geodesic net. A surface carrying a Voss net is called a Voss surface. On a minimal surface a Voss net is isotropic. Every Voss net on a two-dimensional surface is a principal base of a deformation of the surface. Only the helicoid carries an infinite set of Voss nets. The question of whether there are surfaces that carry Voss nets was posed by A. Voss [1].


[1] A. Voss, "Ueber diejenigen Flächen, auf denen zwei Scharen geodätischer Linien ein conjugirtes System bilden", Sitzungsber. Bayrischen Akad. Wiss. München Math.-Naturwiss. Kl. , 18 (1888) pp. 95–102 Zbl 20.0778.02
[2] S.P. Finikov, "Deformation over a principal base and related problems in geometry", Vereinigt. Wiss.-Techn. Verl. 176 S., 5 Abb., Moscow-Leningrad (1937) (In Russian) Zbl 0018.04002
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Voss net. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article