# Potential net

From Encyclopedia of Mathematics

*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