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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:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016900/b0169001.png" /></td> </tr></table>
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$$
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ds  ^ {2}  =
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\frac{du  ^ {2} +dv  ^ {2} }{(U+V)  ^ {2} }
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,
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$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016900/b0169002.png" />. Studied by O. Bonnet in 1848.
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where $  U = U(u), V = V(v) $.  
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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
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article