Parabolic Point

A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of the principal curvatures kappa_1,kappa_2 equals 0.

See also

Anticlastic, Elliptic Point, Gaussian Curvature, Hyperbolic Point, Planar Point, Synclastic

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Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 375, 1997.

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Parabolic Point

Cite this as:

Weisstein, Eric W. "Parabolic Point." From MathWorld--A Wolfram Web Resource.

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