# Definition:Riemannian Density

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## 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**.

## Sources

- 2018: John M. Lee:
*Introduction to Riemannian Manifolds*(2nd ed.): $\S 2$: Riemannian Metrics. Basic Constructions on Riemannian Manifolds