# Difference between revisions of "Apolar nets"

From Encyclopedia of Mathematics

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− | Two nets given in the same domain | + | {{TEX|done}} |

+ | Two nets given in the same domain $G$ of a two-dimensional manifold, where at each point $x\in G$ the tangent directions of one net harmonically subdivide the tangent directions of the other. Thus, for instance, the [[Asymptotic net|asymptotic net]] on a surface in a Euclidean space is apolar with respect to the net of curvature lines (cf. [[Curvature lines, net of|Curvature lines, net of]]). |

## Latest revision as of 07:30, 23 August 2014

Two nets given in the same domain $G$ of a two-dimensional manifold, where at each point $x\in G$ the tangent directions of one net harmonically subdivide the tangent directions of the other. Thus, for instance, the asymptotic net on a surface in a Euclidean space is apolar with respect to the net of curvature lines (cf. Curvature lines, net of).

**How to Cite This Entry:**

Apolar nets.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Apolar_nets&oldid=18746

This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article