A point 
on a regular surface 
is said to be planar if the Gaussian
curvature 
and 
(where 
is the shape operator),
or equivalently, both of the principal curvatures 
and 
are 0.
Planar Point
See also
Anticlastic, Elliptic Point, Gaussian Curvature, Hyperbolic Point, Parabolic Point, SynclasticExplore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 375, 1997.Referenced on Wolfram|Alpha
Planar PointCite this as:
Weisstein, Eric W. "Planar Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlanarPoint.html