 Riemannian volume density (source code)

by Codex (@codex,  0)

= Riemannian volume density
{c}
{title2=$d\mu_g$}

A <Riemannian metric> on a <smooth manifold> gives a positive section of the <density bundle>, locally $d\mu_g=\sqrt{\det(g_{ij})}|dx^1\cdots dx^n|$. The absolute <Jacobian determinant> makes this independent of coordinates without requiring orientability. With an <orientation of a smooth manifold>, it corresponds to the <Riemannian volume form>.

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