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"http://wwwinformationdelightinfo/encyclopedia/entry/determinant" class="copylinks">Determinant of the Metric Tensor on the manifold The <math>dx^i</math> are the 1-form s providing a basis for the Cotangent Bundle of the manifold
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Thus, in either coordinate system, the volume form takes the same expression: the expression of the volume form is invariant under a change of coordinates.
Note that there was nothing particular to two dimensions in the above presentation; the above trivially generalizes to arbitrary dimensions.
- Michael Spivak , ''Calculus on Manifolds'', (1965) W.A. Benjamin, Inc. Reading, Massachusetts ISBN 0-8053-9021-9 ''(Provides an elementary introduction to the modern notation of differential geometry, assuming only a general calculus background)''
