A net that is cut out on the focal surface of a congruence of lines (a hyperbolic one) by enveloping surfaces of that congruence. A focal net of a congruence is a conjugate net. One family of lines of it consists of the cusps of one family of enveloping surfaces of the congruence; the other family is formed by the lines where the enveloping surfaces of the other family are tangent to the focal surface. Every conjugate net on a two-dimensional surface is a focal net of the congruence of tangents to the lines of one of the families of that net. Every hyperbolic congruence of lines has two focal nets.

References

[1] S.P. Finikov, "Theorie der Kongruenzen" , Akademie Verlag (1959) (Translated from Russian)
How to Cite This Entry:
Focal net of a congruence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Focal_net_of_a_congruence&oldid=51070
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article