# Polar correspondence

From Encyclopedia of Mathematics

A correspondence between two surfaces such that at corresponding points the radius vector of one of them is parallel to the normal of the other, and vice versa. For every smooth surface in with radius vector there exists (under certain conditions) a surface polar with it and with radius vector , where is the normal and is the support function to , so that

Sometimes these conditions are also included in the definition of a polar correspondence.

The concept of polar correspondence shows itself particularly clearly (in the sense of a complete duality) in centro-affine geometry.

**How to Cite This Entry:**

Polar correspondence.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Polar_correspondence&oldid=14085

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article