From Wikipedia, the volume of a small ball in an $n$-dimensionl Riemannian manifold M satisfies
$$\frac{Vol(B(\epsilon, p)\subset M)}{Vol(B(\epsilon, 0)\subset \mathbb{R}^n)} = 1 - \frac{S_p}{6(n+2)}\epsilon^2 + O(\epsilon^3)$$
where $p\in M$ and $S_p$ is the scalar curvature of $M$ at $p$. My question is: what does the $O(\epsilon^3)$ term depend on? Does it just depend on curvature, or is it more complicated?
Thank you!