A tangent vector is a principal vector iff

where , , and are coefficients of the first fundamental form and , , of the second fundamental form.

A tangent vector is a principal vector iff

where , , and are coefficients of the first fundamental form and , , of the second fundamental form.

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