In differential geometry, especially the theory of space curves, the Darboux vector is the angular velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it. It is also called angular momentum vector, because it is directly proportional to angular momentum.
In terms of the Frenet–Serret apparatus, the Darboux vector ω can be expressed as
:<math> \boldsymbol{\omega} = \tau \mathbf{T} + \kappa \mathbf{B} \qquad \qquad (1)</math>
and it has the following symmetrical properties: