Holonomic basis

In mathematics and mathematical physics, a holonomic basis or coordinate basis for a differentiable manifold is a set of basis vector fields {e_k} such that some coordinate system {x^k} exists for which

$e_k = {\partial \over \partial x^k}$

A local condition for a basis {e_k} to be holonomic is that all mutual Lie derivatives vanish:

$[e_i,e_j]=0$

A basis that is not holonomic is called a non-holonomic or non-coordinate basis.

See also

• Jet bundle
• Tetrad formalism
• Ricci calculus