This is a very elementary question,
What is the definition for a volume form (or $n$-form) to be parallel with respect to the metric? To find out more about the concept, what kind of topic do I need to look up in standard textbooks?
Many thanks for your help!
It simply means that $\nabla \omega = 0$, where $\omega$ is the volume form and $\nabla$ is the Levi-Civita connection. See also this question on math overflow.