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PLANAR POINT

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