Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 309 / 1 / c / Solution

The vector $T^a$ is the tangent to a reference member of a one-parameter family of affinely parametrized geodesics. The Jacobi field $Y^a$ is the infinitesimal connecting vector from that geodesic to a neighboring one at equal parameter. The geodesic deviation equation states that curvature determines their relative acceleration.