Potential net

Egorov net

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

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

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. D.F. Egorov was the first (1901) to consider potential nets.

References

[1]	D.F. Egorov, "Papers in differential geometry" , Moscow (1970) (In Russian)
[2]	V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)