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 ${\omega }^a$ of the cotangent space is

${\omega }^a=d{x}^a.$

References

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