A moving frame along a curve or submanifold is a smoothly varying ordered basis of the ambient tangent space attached to each point. For a regular space curve parametrized by arc length, the Frenet frame is the moving orthonormal basis consisting of the tangent, normal, and binormal vectors. Differentiating a moving frame expresses its variation through connection forms and converts geometric invariants into differential equations.
Moving Frame
See also
Frenet Formulas, Orthonormal Basis, Tangent SpaceExplore with Wolfram|Alpha
References
Cartan, E. Geometry of Riemannian Spaces. Brookline, MA: Math Sci Press, 1983.Cite this as:
Weisstein, Eric W. "Moving Frame." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MovingFrame.html