Oriented manifold

Riemannian volume form

Let be an oriented -dimensional semi-Riemannian manifold with metric tensor . The Riemannian volume form is a canonical Volume form

which given a chart is defined as

where is the determinant of the metric tensor.

Proof this is well-defined

#missing/proof It suffices to show that abides the Tensor field transformation laws.

See also Hodge star.


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