# Ridge (differential geometry)

In differential geometry, a smooth surface in three dimensions has a **ridge point** when a line of curvature has a local maximum or minimum of principal curvature. The set of ridge points form curves on the surface called **ridges**.

The ridges of a given surface fall into two families, typically designated *red* and *blue*, depending on which of the two principal curvatures has an extremum.

At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines passing through the umbilic, and the other has one line passing through it.

Ridge lines correspond to cuspidal edges on the focal surface.

## See also

## References

- Porteous, Ian R. (2001). "Ridges and Ribs".
*Geometric Differentiation*. Cambridge University Press. pp. 182–197. ISBN 0-521-00264-8.

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