## Darboux Vector

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, T the Tangent Vector, and B the Binormal Vector. The Darboux vector field satisfies
 (2) (3) (4)

See also Binormal Vector, Curvature, Tangent Vector, Torsion (Differential Geometry)

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 151, 1993.

© 1996-9 Eric W. Weisstein
1999-05-24