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Parabolic Point

A point ${\bf p}$ on a Regular Surface $M\in\Bbb{R}^3$ is said to be parabolic if the Gaussian Curvature $K({\bf p})=0$ but $S({\bf p})\not= 0$ (where $S$ is the Shape Operator), or equivalently, exactly one of the Principal Curvatures $\kappa_1$ and $\kappa_2$ is 0.

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


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 280, 1993.

© 1996-9 Eric W. Weisstein