Jacobi field

In Riemannian geometry, a Jacobi field is a vector field along a geodesic ${\displaystyle \gamma }$ in a Riemannian manifold describing the difference between the geodesic and an "infinitesimally close" geodesic. In other words, the Jacobi fields along a geodesic form the tangent space to the geodesic in the space of all geodesics. They are named after Carl Jacobi.