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''Egorov net''

An [[Orthogonal net|orthogonal net]] on a two-dimensional surface in Euclidean space that is mapped to itself by the potential motion of a fluid on this surface. In parameters of the potential net the line element of this surface has the form

$$ 
d s  ^ {2}  =  
\frac{\partial  \Phi }{\partial  u }
 \ 
d u  ^ {2} + 
\frac{\partial  \Phi }{\partial  v }
  d v  ^ {2} ,
$$

where  $  \Phi = \Phi ( u , v ) $
is the potential of the velocity field of the fluid. Each orthogonal semi-geodesic net is potential. A particular case of a potential net is a [[Liouville net|Liouville net]]. D.F. Egorov was the first (1901) to consider potential nets.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  D.F. Egorov,   "Papers in differential geometry" , Moscow  (1970)  (In 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></table>