Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 11E / i

A regularly parametrized curve $\gamma$ on an embedded surface $\Sigma$ is a geodesic when its covariant acceleration vanishes. Equivalently, in the ambient Euclidean space,for an affine geodesic parameter. A complete geodesic is one whose maximal affine parameter interval is all of $\mathbb{R}$.