Guichard congruence

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A congruence of straight lines whose focal nets are formed by the curvature lines of the focal surfaces. One of the surfaces of centres of curvature of each focal surface carries a focal net consisting of geodesic lines. The spherical image of the developable surfaces of a Guichard congruence is a Chebyshev net. The focal surfaces of a Guichard congruence are called Guichard surfaces. Guichard congruences are named after G. Guichard (1889), who was the first to consider them.


[1] S.P. Finikov, "Theorie der Kongruenzen" , Akademie Verlag (1959) (Translated from Russian)
[2] V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)



[a1] G. Guichard, "Surfaces rapporteés à leurs lignes asymptotiques et congruences rapporteés à leurs développables" Ann. Sc. Ec. Norm. Sup. (3) , 6 (1889) pp. 333–348
How to Cite This Entry:
Guichard congruence. V.T. Bazylev (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098