Coordinate-induced basis

In mathematics, a coordinate-induced basis is a basis for the tangent space or cotangent space of a manifold that is induced by a certain coordinate system. Given the coordinate system x^a, the coordinate-induced basis e_a of the tangent space is given by

$e_a = \frac{\partial}{\partial x^a}$

and the dual basis ω^a of the cotangent space is

$\omega^a=dx^a. \,$

References

• D.J. Hurley, M.A. Vandyck Topics in Differential Geometry: a New Approach Using D-Differentiation (2002 Springer) p. 5

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