Planar point

Definition

A point on a regular surface is termed a planar point if it satisfies the following equivalent conditions:

• Both the principal curvatures at the point are zero
• The mean curvature and the Gaussian curvature at the point are zero
• The shape operator is the zero operator

Relation with other properties

Weaker properties

• Umbilic point

Other related properties

• Elliptic point
• Parabolic point
• Hyperbolic point

Related surface properties

• Flat surface
• Synclastic
• Anticlastic