Asymptotic Direction

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes.

1. There are no asymptotic directions at an elliptic point.

2. There are exactly two asymptotic directions at a hyperbolic point.

3. There is exactly one asymptotic direction at a parabolic point.

4. Every direction is asymptotic at a planar point.

See also

Asymptotic Curve

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Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 364 and 418, 1997.

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Asymptotic Direction

Cite this as:

Weisstein, Eric W. "Asymptotic Direction." From MathWorld--A Wolfram Web Resource.

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