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:^[1]

[e_{i},e_{j}]=0

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

References

↑ Roger Penrose; Wolfgang Rindler, Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields, Cambridge University Press, pp. 197–199

See also

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