An 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
where 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. D.F. Egorov was the first (1901) to consider potential nets.
|||D.F. Egorov, "Papers in differential geometry" , Moscow (1970) (In Russian)|
|||V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)|
Potential net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Potential_net&oldid=18915