the manifold according to that form. An oriented pseudo-Riemannian manifold has a natural volume form. In local coordinates, it can be expressed as where the are 1-forms that form a positively oriented basis for the cotangent bundle of the manifold, and is the determinant of the matrix representation of the metric tensor on the manifold in terms of the same basis. Derived quantities Density is the substance's mass per unit volume, or total mass divided by total volume. Specific volume is total volume divided by mass, or the inverse of density. The volumetric flow rate or discharge is the volume of fluid which passes through a given surface per unit time. The volumetric heat capacity is the heat capacity of the substance divided by its volume. See also Baggage allowance Banach–Tarski paradox Dimensional weight Dimensioning Notes References External links