Difference between revisions of "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|Chebyshev net]]. The focal surfaces of a Guichard congruence are called Guichard surfaces. Guichard congruences are named after | + | 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|Chebyshev net]]. The focal surfaces of a Guichard congruence are called Guichard surfaces. Guichard congruences are named after C. Guichard (1889), who was the first to consider them. |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <table> |
| − | + | <TR><TD valign="top">[1]</TD> <TD valign="top"> S.P. Finikov, "Theorie der Kongruenzen" , Akademie Verlag (1959) (Translated from Russian)</TD></TR> | |
| − | + | <TR><TD valign="top">[2]</TD> <TD valign="top"> V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)</TD></TR> | |
| − | + | <TR><TD valign="top">[3]</TD> <TD valign="top"> C. Guichard, "Surfaces rapportées à leurs lignes asymptotiques et congruences rapportées à leurs développables" ''Ann. Sc. Ec. Norm. Sup. (3)'' , '''6''' (1889) pp. 333–348 {{ZBL|21.0764.01}}</TD></TR> | |
| − | + | </table> | |
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Latest revision as of 07:48, 17 July 2025
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 C. Guichard (1889), who was the first to consider them.
References
| [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) |
| [3] | C. Guichard, "Surfaces rapportées à leurs lignes asymptotiques et congruences rapportées à leurs développables" Ann. Sc. Ec. Norm. Sup. (3) , 6 (1889) pp. 333–348 Zbl 21.0764.01 |
How to Cite This Entry:
Guichard congruence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Guichard_congruence&oldid=11913
Guichard congruence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Guichard_congruence&oldid=11913
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article