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PLANAR POINT

A planar 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