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Principal Vector


A tangent vector v_(p)=v_1x_u+v_2x_v is a principal vector iff

 det[v_2^2 -v_1v_2 v_1^2; E F G; e f g]=0,

where e, f, and g are coefficients of the first fundamental form and E, F, G of the second fundamental form.


See also

Fundamental Forms, Principal Curve

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References

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

Referenced on Wolfram|Alpha

Principal Vector

Cite this as:

Weisstein, Eric W. "Principal Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipalVector.html

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