View source for Umbilical point

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



====Comments====
At flat points (cf. [[Flat point|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====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  N.J. Hicks,   "Notes on differential geometry" , v. Nostrand  (1965)</TD></TR></table>