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.

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