Namespaces
Variants
Actions

Umbilical point

From Encyclopedia of Mathematics
Revision as of 17:18, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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