# Potential net

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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)
How to Cite This Entry:
Potential net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Potential_net&oldid=48263
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article