# Umbilical point

From Encyclopedia of Mathematics

An elliptic point of a surface at which the osculating paraboloid degenerates into a paraboloid of revolution. At an umbilical point the normal curvatures in all directions are equal, and the Dupin indicatrix is a circle. An umbilical point is sometimes called a spherical point or circular point.

#### Comments

At flat points (cf. Flat point) the osculating paraboloid degenerates to a plane. Often flat points are also called umbilical. However, the Dupin indicatrix is not defined at flat points.

#### References

[a1] | N.J. Hicks, "Notes on differential geometry" , v. Nostrand (1965) |

**How to Cite This Entry:**

Umbilical point. D.D. Sokolov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Umbilical_point&oldid=16726

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098