The Jacobi Equation describes the behavior of Jacobi fields along a family of geodesics in a Riemannian manifold. It provides a way to understand how geodesics deviate from each other in the presence of curvature, which is essential for studying the stability and properties of geodesic paths. The Jacobi Equation is pivotal in understanding geodesic behavior and underlies significant results like the Rauch comparison theorem.
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