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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:

$$ 
ds  ^ {2}  =  
\frac{du  ^ {2} +dv  ^ {2} }{(U+V)  ^ {2} }
 ,
$$

where  $  U = U(u), V = V(v) $. 
Studied by O. Bonnet in 1848.