  As an example consider the transformation laws for the 4-velocity and the 4-acceleration. Recall that a curve in the four-dimensional spacetime manifold \(M\) is a map \(\gamma : \mathbb{R} \rightarrow M\). For convenience we restrict our attention to those curves which satisfy \(\gamma(0) = p\). If we set \(\gamma^{i} = x^{i} \circ \gamma(0)\), then the components of the 4-velocity and 4-acceleration at \(p \in M\) are respectively given by 