A tangent vector 
is a principal vector iff
![det[v_2^2 -v_1v_2 v_1^2; E F G; e f g]=0,](/images/equations/PrincipalVector/NumberedEquation1.svg) |
where 
,
, and 
are coefficients of the first fundamental
form and 
,
, 
of the second fundamental
form.
Principal Vector
See also
Fundamental Forms, Principal CurveExplore with Wolfram|Alpha
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 VectorCite this as:
Weisstein, Eric W. "Principal Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipalVector.html