Planar Point

A point p on a Regular Surface $M\in\Bbb{R}^3$ is said to be planar if the Gaussian Curvature $K({\bf p})=0$ and $S({\bf p})=0$ (where $S$ is the Shape Operator), or equivalently, both of the Principal Curvatures $\kappa_1$ and $\kappa_2$ are 0.

See also Anticlastic, Elliptic Point, Gaussian Curvature, Hyperbolic Point, Parabolic Point, Synclastic

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 280, 1993.