coordinate cobasis

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A cotangent basis derived from the coordinates x^i\, is known as a coordinate cobasis. In this case, we may write

\tilde{e}^i = dx^i\,.

Given an associated coordinate basis \vec{e}_i = \frac{\partial}{\partial x^i}\,, note that

\vec{e}_i ( \tilde{e}^j ) = \frac{\partial}{\partial x^i} ( dx^j ) = \frac{\partial x^j}{\partial x^i} = \delta^j_i\,.
Retrieved from "http://www.mathematics.thetangentbundle.net/wiki/Differential_topology/coordinate_cobasis"
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