Jacobi Fields: Curvature, Conjugate Points, and the Stability of Geodesics

We unpack Jacobi fields along geodesics as the link between curvature and how nearby paths behave. From the sphere’s converging/diverging geodesics to negative curvature and chaotic divergence, we explore the Jacobi equation, conjugate points, and how these ideas illuminate stability, shortest paths, and even concepts in general relativity.

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