The rotation vector of the trihedron of a curve with curvature when a point moves along a curve with unit speed. It is given by

(1)

where is the torsion, the tangent vector, and the binormal vector. The Darboux vector field satisfies

			(2)
			(3)
			(4)

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 205, 1997.

CITE THIS AS:

Weisstein, Eric W. "Darboux Vector." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DarbouxVector.html