Difference between revisions of "Bonnet net"
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An [[Isothermal net|isothermal net]] whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is: | An [[Isothermal net|isothermal net]] whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is: | ||
| − | + | $$ | |
| + | ds ^ {2} = | ||
| + | \frac{du ^ {2} +dv ^ {2} }{(U+V) ^ {2} } | ||
| + | , | ||
| + | $$ | ||
| − | where | + | where $ U = U(u), V = V(v) $. |
| + | Studied by O. Bonnet in 1848. | ||
Latest revision as of 10:59, 29 May 2020
An isothermal net whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is:
$$ ds ^ {2} = \frac{du ^ {2} +dv ^ {2} }{(U+V) ^ {2} } , $$
where $ U = U(u), V = V(v) $. Studied by O. Bonnet in 1848.
How to Cite This Entry:
Bonnet net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bonnet_net&oldid=46104
Bonnet net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bonnet_net&oldid=46104
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article