Jacobi Field

(Riemannian Geometry)


Riemannian Geometry
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What is Jacobi field?

In Riemannian geometry, a Jacobi field is a vector field along a geodesic 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.

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Jacobi equationJacobi vector field


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 — Date merged: 11/6/2021, 1:32:53 PM
 — Date scraped: 5/20/2021, 6:19:55 PM