# Definition:Riemannian Density

## Definition

Let $\struct {M, g}$ be an $n$-dimensional Riemannian manifold.

Let $\tuple {E_i}$ be an local orthonormal frame.

Let $\mu$ be a positive smooth density such that:

$\forall \tuple {E_i} : \map \mu {E_1, \ldots, E_n} = 1$

Then $\mu$ is known as the Riemannian density.