In mathematics, a holonomic basis for a manifold is a set of basis vectors e_k for which all Lie derivatives vanish:

[e_j,e_k] = 0

Some authors (confusingly) call a holonomic basis a coordinate basis, and an anholonomic basis a non-coordinate basis. Spherical and cylindrical coordinates are an example of basis with non-vanishing commutators.

See also

• Jet bundle