A planar point (or level point) of a surface is a non-singular point where the principal curvatures are equal to zero (see notations).
Equivalent conditions:
    - all the normal planar sections have zero curvature.
    - all the planar sections passing by the point have zero curvature.
    - the second quadratic form is equal to zero.
Examples:
    - all the points of a plane (and conversely, a surface all the points of which are planar points is a portion of a plane)
    - the point of the axis of a surface of revolution obtained by rotating a curve with a zero curvature point around a perpendicular axis passing by this point.
    - The center of a monkey saddle.
 
 

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© Robert FERRÉOL 2017