In Riemannian geometry, a Jacobi field is a vector field along a geodesic γ {\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.
In Riemannian geometry, a Jacobi field is a vector field along a geodesic γ {\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.
Source: Wikipedia "Jacobi field" · CC BY-SA 4.0
Share this article: X · Bluesky