Difference between revisions of "Voss net"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A. Voss, ''Sitzungsber. Bayrischen Akad. Wiss. München Math.-Naturwiss. Kl.'' , '''18''' (1888) pp. 95–102</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> S.P. Finikov, "Deformation over a principal base and related problems in geometry" , Moscow-Leningrad (1937) (In Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> 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}}</TD></TR> | ||
| + | <TR><TD valign="top">[2]</TD> <TD valign="top"> 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}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 17:25, 31 March 2018
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].
References
| [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 |
How to Cite This Entry:
Voss net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Voss_net&oldid=43052
Voss net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Voss_net&oldid=43052
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article